Question

The owner of a​ health-food store sells dried apples for ​$1.30 per​ quarter-pound, and dried apricots for ​$1.60 per​ quarter-pound. How many pounds of each must he mix together to get 20 lb of a mixture that sells for ​$1.51 per​ quarter-pound?

Answer 1

To find out how many pounds of dried apples and dried apricots the owner needs to mix to get 20 pounds of a mixture that sells for $1.51 per quarter-pound, we can set up a system of equations.

Step-by-step explanation:

To find out how many pounds of dried apples and dried apricots the owner needs to mix to get 20 pounds of a mixture that sells for $1.51 per quarter-pound, we can set up a system of equations.

Let's say the amount of dried apples in pounds is a, and the amount of dried apricots in pounds is b.

We know that the price per quarter-pound of dried apples is $1.30, so the price per pound of dried apples is $1.30 * 4 = $5.20. Similarly, the price per pound of dried apricots is $1.60 * 4 = $6.40.

The total cost of the mixture is given by the equation 5.20a + 6.40b = 1.51 * 20 * 4.

The total weight of the mixture is given by the equation a + b = 20.

We can solve this system of equations to find the values of a and b.

Answer 2

6 pounds of dried apples and 14 pounds of dried apricots

Step-by-step explanation:

A = dried apples

B = dried apricots

1.3A + 1.6B = 1.51 x 20 = 30.2

A + B = 20

A = 20 - B

Replace A:

1.3(20 - B) + 1.6B = 30.2

26 - 1.3B + 1.6B = 30.2

0.3B = 30.2 - 26 = 4.2

B = 4.2 / 0.3 = 14

A = 6