Question

A mistake was made in mixing the lemonade—
PLEASE HELP!!

Answer 1

Part A:

`4 + x = y`

`0.5*4 + 1*x = 0.7*y`

`x = 8/3\ quarts\ of\ 100\%\ solution`

`y = 20/3\ quarts\ of\ 70\%\ solution`

Part B:

`x + y = 10`

`2x + 3y = 23`

`x = 7` and
`y = 3`

Explanation:

Part A:

The inicial concentration of the lemonade is 50%, and the volume is 4 quarts, and we will add x quarts of a lemonade with a concentration of 100%, so the total volume will be y, and the concentration will be 0.7, so we have that:

`4 + x = y`

`0.5*4 + 1*x = 0.7*y`

Using the value of y from the first equation in the second one, we have:

`2 + x = 0.7*(4 + x)`

`2 + x = 2.8 + 0.7x`

`0.3x = 0.8`

`x = 8/3\ quarts`

`y = 4 + 8/3 = 20/3\ quarts`

Part B:

If he shoots a total of ten targets, we can write the equation:

`x + y = 10`

Each stationary target is 2 points, and each moving target is 3 points, so if the total points is 23, we have:

`2x + 3y = 23`

If we subtract the second equation by two times the first one, we have:

`2x + 3y - 2*(x + y) = 23 - 2*10`

`2x + 3y - 2x - 2y = 23 - 20`

`y = 3`

`x + 3 = 10` ⇒
`x = 7`