For the following word problems:
Set up two equations by letting x and y be the two numbers. Use x as the first of the two numbers.
Solve for x by adding the two equations.
Solve for y.
The sum of the first number and the second number is 14 and the difference between four times the first number and six times the second number is 6.
The sum of two numbers is 56 and their difference is 30.
Seven times the first number is added to the second number to get 64 and the difference between three times the first number and the second number is 16.
The length of a rectangle measures 12 units more than the width, and the perimeter of the rectangle is 56 units.
Let y be the width and x be the length of the rectangle.
Use the fact that the length of the rectangle is 12 units more than the width to set up an equation relating x and y.
Use the fact that the perimeter of the rectangle is equal to 56 to set up another equation relating x and y.
Use simultaneous equations to solve for x and y.
There are 36 members in a group, and the men outnumber the women by 16.
Let x and y be the number of women and men in the group respectively.
Use the fact that the men outnumber the women by 16 to set up an equation relating x and y.
Use the fact that there are a total of 36 members in the group to form another equation relating x and y.
Use simultaneous equations to solve for x and y.
When comparing some test results Christa noticed that the sum of her Geography test score and Science test score was 172, and that their difference was 18.
Given that her Geography score is x and her Science score is y and she scored higher for the Geography test:
Use the sum of the test scores to form an equation.
Use the difference of the test scores to form another equation.
Use these two equations to find her Geography score.
Find her Science score.
A mother is currently 10 times older than her son. In 3 years time, she will be 7 times older than her son.
Let x and y be the present ages of the son and mother respectively.
Use the fact that the mother is currently 10 times older than her son to set up an equation relating x and y.
Use the fact that the mother will be 7 times older than her son in 3 years time to set up another equation relating x and y.
Use simultaneous equations to solve for x and y.
A man is five times as old as his son. Four years ago the man was nine times as old as his son. Let x and y be the ages of the man and his son respectively.
Use simultaneous equations to solve for x and y.
Toby's piggy bank contains only 5 cent and 10 cent coins. If it contains 70 coins with a total value of \$3.85, find the number of each type of coin.
Let x and y be the number of 5 cent and 10 cent coins respectively.
Use simultaneous equations to solve for x and y.
Christa has \$4000 to invest, and wants to split it up between two accounts:
Account A which earns 7\%annual interest.
Account B which earns 8\% annual interest.
Her target is to earn \$303 total interest from the two accounts in one year.
Let x and y be the amounts, in dollars, that she invests in accounts A and B respectively.
Using the fact that she has \$4000 to invest between the two accounts, write an equation in terms of x and y.
Using the fact that she wants to earn total interest of \$303, write an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Patricia has \$18\,000 to invest, and wants to split it up between two accounts:
Account A which earns 8\% annual interest.
Account B which earns 7\% annual interest.
Her target is to earn \$1353 total interest from the two accounts in one year.
Let x and y be the amounts, in dollars, that she invests in accounts A and B respectively.
Using the fact that she has \$18\,000 to invest between the two accounts, write an equation in terms of x and y.
Using the fact that she wants to earn total interest of \$1353, write an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Oprah invested \$16\,000 in total in two stocks A and B. In one year, the investment in stock A made a 14\% return, while the investment in stock B fell by 6\%. The total annual interest from both stocks was \$700.
Let x and y be the amounts, in dollars, that she invested in stocks A and B respectively.
Using the fact that she invested \$16\,000 in total, write an equation in terms of x and y.
Using the fact that she earned total interest of \$700, write an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
A bank loaned out \$12\,000, part of it at a rate of 7\% per year and the rest at the rate of 13\% per year. The interest received for the year totalled \$1158.
Let x and y be the amounts, in dollars, that are loaned at the rates of 7\% and 13\% respectively.
Using the fact that the total amount loaned was \$12\,000, write an equation in terms of x and y.
Using the fact that the total interest earned was \$1158, write an equation in terms of x and y.
Solve for y, the amount the bank had loaned at a rate of 13\%. Give your answer to the nearest dollar.
Solve for x, the amount the bank loaned at a rate of 7\%. Give your answer to the nearest dollar.
The number of new jobs created in Wyndburn varies greatly each year. The number of jobs created in 2012 was 260\,000 less than triple the number of jobs created in 2007. This is equivalent to an increase of 480\,000 jobs created from 2007 to 2012.
Let x be the number of jobs created in 2007 and let y be the number of jobs created in 2012.
Set up two equations, in terms of. x and y, that describe the statements above.
Use simultaneous equations to solve for x and y.
20 pens and 3 rulers cost \$86 while 4 pens and 15 rulers cost \$46.
Let x and y be the price of the pen and ruler respectively.
Use the fact that 20 pens and 3 rulers cost \$86 to write an equation in terms of x and y.
Use the fact that 4 pens and 15 rulers cost \$46 to write an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Luke bought some fresh produce. He picked up 2 oranges, and 3 bananas. The cost of the Luke’s shopping was \$18.30.
Valentina also went to the same shop and bought 5 oranges and 7 bananas. The cost of the Valentina’s shopping was \$44.03.
If the price of oranges is represented by f and the price of bananas is represented by g, write an equation for Luke's shopping trip.
Write an equation to represent Valentina's shopping trip, then rearrange to find the value of g in terms of f.
Hence, find the price of oranges.
Finally, find the price of bananas.
The total cost of 9 sharpeners and 5 sketchbooks is \$31.55. If the cost of a sharpener is \$a, and a sketchbook is \$2.25 more expensive. Find the value of a.
Valentina has \$5.50 of change in her pocket. She has only 20 cent and 50 cent coins, adding to 14 coins in total. If t is the number of 20c coins that Valentina has, find t.
A rectangular garden bed has a perimeter of 13.2 meters and the length is 3.4 metres longer than the width.
If the width of the fixture is w metres, find w to one decimal place.
Hence, find the length of the garden bed.
Maria and Buzz both walk from their houses to the bus stop every morning. Maria walks 1.5 kilometres further then Buzz, and together they walk 3.3 kilometres.
If Buzz walks a distance of m kilometres find the value of m.
James travels in a cab on Monday and is charged \$5.90. On Tuesday the return trip travelling a different route cost \$13.90. The fare is made up of an initial fixed fee and the kilometre meterage. The return trip was 16\text{ km} longer.
If the initial fixed fee is \$c, the meterage is \$k per kilometre and the trip was x kilometres on Monday, write an equation to represent Monday's trip and rearrange for c.
Write a similar expression to represent the trip on Tuesday, then solve for k. Leave your answer to two decimal places.
If the length of Monday's trip was 8 kilometres, solve for c. Leave your answer to two decimal places.
The function f \left( x \right) = 0.47 x + 8.9 represents the U.S. annual bottled water consumption (in billions of gallons) and the function g \left( x \right) = - 0.17 x + 14.2 represents the U.S. annual soda consumption (in billions of gallons). For both functions, x is the number of years since 2009, and these functions are appropriate for the years 2009 to 2013.
Using the system formed by these functions, solve for x. Round your answer to the nearest whole number.
Hence, predict the year in which the bottled water and soda consumption will be the same.
Consider the triangle below:
Angle x is double the size of angle y. Write an equation to represent in terms of x and y to represent this.
Write an equation, in terms of x and y, using the angle sum of a triangle.
Use simultaneous equations to solve for x and y.
Consider the diagram of the rectangle below:
Use the fact that A B = C D to set up an equation in terms of x and y.
Use the fact that A D = B C to set up an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Find the length of the rectangle.
Find the width of the rectangle.
Consider the following diagram of a kite:
Use the fact that A B = B C to set up an equation in terms of x and y.
Use the fact that A D = C D to set up an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Find the length of the shorter side.
Find the length of the longer side.
Consider the parallelogram below:
Use the fact that A M = D M to set up an equation in terms of x and y.
Use the fact that C M = B M to set up an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Find the length of A M.
Find the length of side C M.
The perimeter of the triangle below is 56\text{ cm}, and the same values for x and y are used to construct the rectangle shown. The rectangle's length is 8\text{ cm} longer than its width.
Use the rectangle to find x in terms of y.
Use the triangle to find another equation in terms of x and y.
Use simultaneous equations to solve for x and y.
Consider the following triangle:
Use the fact that AB = AC to set up an equation in terms of x and y.
Use the fact that AB = BC to set up an equation in terms of x and y.
Use simultaneous equations to solve for x and y.
