2.03 Rewriting expressions to understand relationships
If Sam is currently x years old, write an expression using x to represent his age after 5 years.
Consider the case when n is even and greater than 2, and m is odd. Determine whether each of the following represents an even number:
3 n + 2 m
8 n + 3 m + 3
2 n + 3 m
7 n + 3 m + 2
m + n
In a particular year, Re-source Waste Recovery produces sewerage treatment plants at a cost of \$u per plant. Re-source Waste Recovery also pays a fee of \$b per year for its use of the production facilities.
Using only addition, write an expression representing the total production cost from 1 year if there are 3 sewerage treatment plants produced in that year.
Write an expression representing the production cost in that year.
A clothing store receives a shipment of jackets and skirts. The jackets come in blue boxes containing 6 jackets each, while the skirts come in red boxes containing 5 skirts each. In this shipment, there are x blue boxes and y red boxes.
Write an expression representing the number of boxes in the shipment.
Write an expression representing the number of clothing items in the shipment.
Tanner has to pay the price of his meal, \$b, plus a 10\% tip. Write an expression representing the price he will pay for his meal including the tip in terms of b.
Jill is 9\text{ cm} taller than Ally, while Melanie is 2\text{ cm} shorter than Ally.
Let v be Ally's height in centimeters.
Write an expression for Jill's height.
Write an expression for Melanie's height.
Emma has \$80 in her wallet. If she spends \$m, how much will she have remaining?
Side B of a triangle is 9\text{ in} longer than side A. Side C is 8\text{ in} shorter than three times the length of side A.
Let y be length of side A.
Write an alegbraic expression for the length of side B.
Write an expression for the length of side C.
A rectangle has a length of (x+6) \text{ m} and a width of 4 \text{ m}. Write an expression for:
The perimeter of the rectangle.
The area of the rectangle.
For a particular airline, each boarding passenger has a checked baggage allowance of 60 pounds and carry on allowance of 30 pounds. To calculate the amount of fuel required for the flight, the airline assumes each passenger weighs 170 pounds on average and that each uses the maximum baggage allowance.
Let x represent the number of passengers boarding the flight.
State whether the following expressions could be used to calculate the total weight of passengers and their luggage on board a flight.
x \times \left(170 + 90\right)
x \times \left(170 + 60 + 30\right)
x \times 170 + x \times 60
260 \times x
170 \times \left(x + 60 + 30\right)
Kostas travels to a foreign country, where the value of currency is described in terms of the variables ‘x’ and ‘y’. When Kostas arrives, he has plenty of the coins worth 2 y each and plenty of the notes worth x + y each, but none of the several other types of coins or notes.
Kostas goes to a cafe to buy a hot breakfast that costs 4x+6y. If he pays using coins worth 2y each and notes worth x+y each, how many coins and notes should he use? Show your work.
How many coins and notes should he use to buy the items that cost the following?
4 x + 8 y
x + 3 y