Question

You have $25 to spend on picking 21 pounds of three different types of apples in an orchard. The Empire apples cost $1.40 a

Answer 1

Answer:

5 pounds of the Empire apples, 14 pounds of the Red Delicious apples, and 2 pounds of the Golden Delicious apples.

Step-by-step explanation:

Let's call the Empire apples weight at E, the Red Delicious at R, and the Golden Delicious at G. We know that the total weight must be 21 pounds so:

R + E + G = 21 (equation 1)

The total amount of spent must be $25, and the price given is per pound, so the priced paid is the cost multiplied by the weight:

1.40*E + 1.10*R + 1.30*G = 25 (equation 2)

And the weight of the Red Delicious must be equal to twice of the combined weight of the others:

R = 2*(E + G)

E + G = R/2 (equation 3)

Let's substitute equation 3 in equation 1

R + R/2 = 21

(2R + R)/2 = 21

3R = 42

R = 14 pounds.

So, E + G = 7

G = 7 - E (equation 4)

Let's substitute the result of R and the equation 4 in the equation 2:

1.40*E + 1.10*14 + 1.30*(7 - E) = 25

1.40E + 15.40 + 9.10 - 1.30E = 25

0.10E = 25 - 24.50

0.10E = 0.50

E = 5 pounds

G = 7 - E

G = 7 - 5

G = 2 pounds.