Question

Sue plans to mix peppermints worth $1.20 per lb with chocolates worth $2.40 per lb to get a 40 lb mix that is worth $1.65 per lb. How much of each should she use?

Answer 1

Answer:

Each should be used as follows:

Weight of peppermints = X = 25 lb

Weight of Chocolates = Y = 15 lb

Explanation:

Suppose

Weight of peppermints = X

Weight of Chocolates = Y

So According to given condition

X + Y = 40 (Eq. 1)

1.2X + 2.4Y = 1.65*40

1.2X + 2.4Y = 66 (Eq. 2)

By multiplying  (Eq. 1) with 1.2 we get

1.2X + 1.2Y = 48  (Eq. 3)

Now by subtracting  (Eq. 2) from  (Eq. 3)

(1.2X + 1.2Y) - (1.2X + 2.4Y) = 48 - 66

1.2X + 1.2Y - 1.2X - 2.4Y = -18

1.2X - 1.2X + 1.2Y - 2.4Y = -18 (Rearrange)

-1.2Y = -18

1.2Y = 18

Y = 18/1.2

Y = 15

By placing value of Y in (Eq. 1)

X + 15 = 40

X = 40 - 15

X = 25

Check

1.2X + 2.4Y = 66

1.2 (25) + 2.4 (15) = 66

66 = 66