Question

Peter Pan works at the Stay Young Factory mixing the “Don’t Grow Up” formula. He is combining chemical A which costs $5.10 an ounce and chemical Z that has a price of $2.10 an ounce. The formula weighs 5 ounces and costs $3.60 per ounce. Peter Pan made the table below to help determine the amount of each chemical for the mix. What is the missing number in the table?

Answer 1

18

Explanation

Step 1

let

x represents the amount of chemical A ( in ounces)

y represents the amount of chemical B ( in ounces)

as the weigth of the formula is 5 ounces

$x+y=5\rightarrow equation(1)$

so, if the cost of Chemical A is $5.1 per ounces, the total cost of the chemical A is

$The\text{ cost of the chemical A=5.1x}$

and if the cost of Chemical Z is $2.1 per ounces, the total cost of the chemical Z is

$The\text{ cost of the chemical Z=2.1y}$

now, the cost of the formula will be

$\begin{gathered} Cost\text{ of chemical A+cost of chemical Z= cost of the formula} \\ 5.1x+2.1y=Cost\text{ of the formula} \end{gathered}$

Step 2

we are told the weigh of the formula is 5 ounces and it cost $3.6 per ounces, so the total cost of the formula is

$\begin{gathered} \cos t\text{ of the formula= rate}\cdot amount\text{ of ounces} \\ \text{Total cost of the formula=3.6 }\frac{dollars}{\text{ounces}}\cdot5\text{ ounces} \\ \text{Total cost of the formula=}18\text{ dollars} \end{gathered}$

now, replace.

$\begin{gathered} 5.1x+2.1y=Cost\text{ of the formula} \\ 5.1x+2.1y=18 \end{gathered}$

so, the missing value in the table is 18

I hope this helps you