Question

Sue has red apples worth 2.30$ per pound and green apples worth 1.90$ a pound How many pounds of each should she mix to get a mixture of 20 pounds worth 2.06$ per pound?

Answer 1

8 pounds of red apples
12 pounds of green apples

Explanation:

The "pounds" is the variable with different cost factors.
The total package of 20 pounds will have a value of
`20 xx 2.06 = 41.20`

The components of this value are from the two apple types:
`41.20 = 2.30 xx W_r + 1.90 xx W_g`
`W_r + W_g = 20` ; `W_r = 20 - W_g`

Substitute this into the overall equation:
`41.20 = 2.30 xx (20 - W_g) + 1.90 xx W_g`

Solve for `W_g`:
`41.20 = 46 - 2.30 xx W_g + 1.90 xx W_g`
`-4.80 = -0.4 xx W_g` ; `W_g = 12`

Solve for `W_r`:
`W_r = 20 - W_g` ; `W_r = 20 - 12 = 8`

CHECK:
`41.20 = 2.30 xx W_r + 1.90 xx W_g`
`41.20 = 2.30 xx 8 + 1.90 xx 12`
`41.20 = 18.40 + 22.80 = 41.20` CORRECT!

Answer 2

Red apples `=8` pounds
Green apples `=12` pounds

Explanation:

Let Red Apples, bought be `x` pounds
Let Green Apples, bought be `y` pounds

Then-

`x + y = 20` in terms of quantity --------------- (1)
`(x xx 2.30) +(y xx 1.90) =20 xx 2.06` in terms of money

`2.3x+1.9y=41.2` ------------ (2)

Solve equation (1) for `x`

`x=20-y`

Substitute `x=20-y` in equation (2)

`2.3(20-y)+1.9y=41.2`
`46-2.3y+1.9y=41.2`
`-0.4y=41.2-46=-4.8`
`y=(-4.8)/(-0.4)=12`

`y= 12`
Substitute `y= 12` in equation (1)

`x+12=20`
`x=20-12=8`
`x=8`

Red apples `=8` pounds
Green apples `=12` pounds