Question

You are making a 2 ingredient trail mix with almonds and raisins. There is a 5:7 ratio of almonds to raisins. How many ounces of almonds would be in a 3-pound bag of this trail mix? (There are 16 ounces in 1 pound.) *​

Answer 1

Answer:

There would be 20 ounces of almonds in the bag

Step-by-step explanation:

System of Equations

To solve the problem, we'll set up these two variables:

x = ounces of almonds

y = ounces of raisins

The ratio of almonds to raisins in the trail mix is 5:7, thus:

$\displaystyle \frac{x}{y}=\frac{5}{7}$

Cross-multiplying:

7x=5y         [1]

A 3-pound bag of this trail mix contains 3*16=48 ounces that include almonds and raisins, thus:

x + y = 48      [2]

Multiplying [2] by 5:

5x + 5y = 240

Substituting from [1]:

5x + 7x = 240

12x = 240

x = 240/12

x = 20

There would be 20 ounces of almonds in the bag