Question

The county pays $0.63 for each pound of aluminum that is collected from a county road. The eighth-grade class picked up 115 pounds of trash in a weekend fund-raiser. How much money did they earn?

Answer 1

The amount of money is $72.45.

Explanation:

`color(blue)("Assumption: All the trash was aluminum.")`

Multiply the mass of aluminum collected by the price per pound.

`115cancel"lb"xx"$0.63"/(1 cancel"lb")=$72.45`

Answer 2

`$72.45`

Explanation:

Meave60 has used the shortcut method to solve this question.

The shortcut is derived from the first principle method and jumps steps. Consequently much quicker. Thus it is worth learning the shortcuts. Very useful in exams!

`color(blue)("Using first principles: ratios")`

write the ration in fraction form giving:

`("payment")/("weight") ->($0.63)/(1 lb) -=("Payment")/(115 lb)`

To change the `1lb` into `115 lb` we multiply by 115

For multiply or divide of ratios, what we do to the bottom we also do to the top.

`=>($0.63xx115)/(1 lbxx115) =("Payment")/(115 lb)`

`color(purple)("What follows is the shortcut")`

So payment received is `$0.63xx115 = $72.45`