Question

Jesse bought 5.2 pounds of grapes for $7.75. Using the unit rate, how much would 3 pounds of grapes cost?

Answer 1

`3` pounds would cost `color(green)($4.47)`

Explanation:

`{:($7.75),("for"),(5.2" pounds"):}rArr{:(($7.75)/(5.2)~~$1.4938),("for"),(1" pound"):}`

So the unit price is `$1.4938` per pound.

`($1.4938)/cancel("pound")xx3cancel(" pounds") = $4.47` (to the nearest cent)

Answer 2

`3lb" of grapes"=$4.47` to 2 decimal places

Explanation:

`color(blue)("Determine unit cost")`

In the context of this question unit rate is the cost of 1 (unit) pound of grapes.

`color(brown)("Using ratio")`

`("cost")/("weight") ->($7.75)/(5.2)" but we need "("cost")/1`

To turn the 5.2 into 1 divide it by 5.2. For multiply or divide, what we do to the bottom we also do to the top to maintain correct proportions.

`("cost")/("weight") ->($7.75)/(5.2) -=($7.75-:5.2)/(5.2-:5.2) = (1.4903...)/1`

To reduce rounding error use `(7.75-:5.2)/1 = 7.75/5.2` as unit cost.
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`color(blue)("Determine cost of 3 pounds of grapes")`

1 pound cost `$7.75/5.2`

`1lb =$7.75/5.2`

Multiply both sides by 3

`3xx1lb=3xx$7.75/5.2`

`3lb=$4.47115....`

`3lb=$4.47` to 2 decimal places