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

Answer:

Small candies $=9$

Extra large candies $=12$

Step-by-step 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

$x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}$

Since number of candies should be integer.

let $x=7,y=13$

total spend $4\times7+12\times13=184$ which is more than $\ 180$, so this combination is not possible.

$let\ x=8,y=12\\8\times4+12\times12=176$

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

Hence  small candy $=9$

extra large candy $=12$