Question

Sammy bought fruit at the farmers market to resell at the school snack stand. she bought a total of 288 pieces of fruit. she bought 4 times as many apples as pears, twice as many peaches as pears, and 5 times as many oranges as pears. let b be the number of pears.Part A drag expressions to represent the number of each type of fruit in the problem.

Answer 1

We want to know how many apples, pears, peaches and oranges Sammy bought. We know that she bought a total of 288 fruits, and:

• 4 times as many apples as pears

,

• 2 times as many peaches as pears

,

• 5 times as many oranges as pears

We will call by a, p and o the amount of apples, peaches and oranges bought, and by b the number of pears. The information above gives us that:

`\begin{gathered} a+p+o+b=288 \\ a=4b \\ p=2b \\ o=5b \end{gathered}`

Replacing the values obtained we get:

`\begin{gathered} 4b+2b+5b+b=288 \\ \text{Solving for b:} \\ 12b=288 \\ b=(288)/(12)=24 \end{gathered}`

This means that the number of pears is 24, and with this we can obtain the other fruits:

`\begin{gathered} a=4b=4(24)=96 \\ p=2b=2(24)=48 \\ o=5b=5(24)=120 \end{gathered}`

Hence, the number of apples is 96, the number of peaches is 48 and the number of oranges is 120.