3.04 Problem solving with equations
Write the following statements as equations, where x represents the number:
Five less than 2 times a number gives 3.
The quotient of 15 and a number is 3.
The product of 3 and a number increased by 4 is 27.
Two times a number is equal to 12 decreased by the number.
Eleven less than 8 times a number is 15.
Five more than triple a number is 29.
The product of 7 and a number increased by 2 is 21.
Three times a number is equal to 3 increased by twice the number.
For each of the following statements:
Write the statement as an equation, where x represents the number.
Solve for the value of x.
The sum of a number and 7 is 17.
Seven more than twice a number is 23.
Fifteen minus three quarters of a number is 9.
Seven times a number is equal to 10 more than twice the number.
Eight divided by a number equals \dfrac{1}{2} times that number.
Three is the difference of a number and 7, divided by 2.
Five less than the quotient of a number and 4 gives 2.
Six is equal to double the difference of a number and 10.
Write the statement "The sum of 8 and 12 x is equal to 92" as an equation and then find the value of x.
Hayley and Aoife donate to charity. Together they donate \$260. If Hayley donated \$ m, and Aoife donated \$105:
Write an equation that represents the relationship between the amounts each donated.
Find the value of m.
A bag contains 80 candies. The candies are shared evenly between 10 children. Let n represent the number of candies each child receives.
Write an equation that represents the relationship between the total number of candies and the number of candies each child receives.
Now, solve the equation.
Justin divides a deck of cards into 7 even piles. There are 12 cards in each pile. Let c represent the total number of cards in the deck.
Write an equation that represents the relationship between the total number of cards in the deck and the number of cards in each pile.
Now, solve the equation.
Tricia gives Tom 25 marbles from her collection. Tricia now has only 44 marbles in her collection. Let m represent the number of marbles she had before giving some away.
Write an equation that represents the relationship between the initial number of marbles and the number of marbles left in her collection.
Now, solve the equation.
The perimeter of a square with side length d \text{ ft} is 40 \text{ ft}.
Write an equation in terms of the side length, d.
Now, find the value of d.
A rectangle has a length of 14 \text{ yd} and an area of 56 \text{ yd}^2. Find w, the width of the rectangle.
Three consecutive integers are such that the sum of the first and twice the second, is 12 more than twice the third. Let x be the smallest of the numbers.
Form an equation and solve it for x.
Find the three consecutive integers.