Question

Julia is going to the store to buy candies. Small candies cost $4 and extra-large candies cost $12.She needs to purchase at least 20 candies, but she cannot spend any more than$180.

Answer 1

Small candies
`=9`

Extra large candies
`=12`

Explanation:

Let small candies
`=x`

Extra large candies
`=y`

the number of candies is at least
`20`.

`x+y\geq20`

Cost of
`1` small candy
`=\$4`

Cost of
`1` extra large candy
`=\$12`

but she has only
`\$180` to spend

`4x+12y\leq180`

Solve for

`x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)*4\\8y=100\\y=(100)/(8) \\y=(25)/(8) \\from\ eqn(1)\\x+(25)/(2)=20\\ x=20-(25)/(2) \\x=(15)/(2)`

Since number of candies should be integer.

let
`x=7,y=13`

total spend
`4*7+12*13=184` which is more than
`\$180`, so this combination is not possible.

`let\ x=8,y=12\\8*4+12*12=176<180`

She has
`\$4` more so she can buy
`1` more small candy.

Hence small candy
`=9`

extra large candy
`=12`