Question

A man sells a type of nut for $7 per pound and a different one for $4.20 per pound, how much of each type should be used to make 24 pound mixture that sells for $5.37

Answer 1

Answer:

type of nut = 10.

Different type of nut = 14.

Explanation:

1 pound = $5.37

24 pound = 5.37 * 24

= $128.88.

Let X be the type of nut and Y be the different one.

Value of the nuts in dollars,

i. 7X + 4.2Y = 128.88

Weight of the nuts in pounds,

ii. X + Y = 24

Rearranging ii,

X = 24 - Y inputting into i,

7(24 - Y) + 4.2Y = 128.88

168 - 7Y + 4.2Y = 128.88

2.8Y = 39.12

Y = 14

Inputting the value of Y into ii,

X = 24 - 14

= 10

Answer 2

a type nut is 10 pounds

a different one is 14 pounds

Explanation:

let a type of the nut be represented by t

Let a different one be represented by d

a type of nut cost $7 per pound

a different one cost $4.20 per pound

The cost of the mixture for 24 pounds = 5.37 * 24

= $128.88

t + d = 24 ........(1)

7t + 4.2d = 128.88 ..........(2)

From equation (1), t = 24 - d

Put t = 24 - d in equation 2

7(24 - d) + 4.2d = 128.88

168 - 7d + 4.2d = 128.88

168 - 2.8d = 128.88

-2.8d = 128.88 - 168

-2.8d = -39.12

d = -39.12 / -2.8

d= 13.97

d = 14 pounds

t = 24 - d

t = 24 - 14

t = 10 pounds

A type nut is 10 pounds. A different one is 14 pounds