Question

Please help! really stuck on this question!

Cameron sponsored a fundraiser that 582 people attended. He raised 6,480. He charged $15 for balcony seats and $10 for ground seats. How many people bought balcony seats (b) and how many bought ground seats (g)?

15b + 10g = 6,480
b + g = 582
​

Answer 1

132 people bought balcony seats and 450 people bought ground seats.

Explanation:

We want to solve the system of equations:

`\left\{ \begin{array}{ll} 15b+10g=6480 \\ b+g=582 \end{array} \right`

We can solve this by using substitution. From the second equation, we can subtract b from both sides:

`g=582-b`

In the first equation, we can divide both sides by five:

`3b+2g=1296`

Substitute:

`3b+2(582-b)=1296`

Distribute:

`3b+1164-2b=1296`

Simplify:

`b+1164=1296`

Solve for b:

`b=132`

Using the modified equation again, substitute:

`g=582-(132)`

Evaluate:

`g=450`

Therefore, 132 people bought balcony seats and 450 people bought ground seats.