Need serious help cant figure it out

Question

A theater sold a total 621 child and adult movie tickets for $2725. a child ticket sold for $3 and an adult ticket for $5. How many child tickets were sold? what was the value of the adult tickets

Answer 1

We have 2 unknowns, so we must find 2 equations to solve for this.

Let x = # of children tickets sold

y = # of adult tickets sold

Eq. I: x + y = 621 total # of tickets sold is 621

Eq. II: 3x + 5y = 2725 $3 for each child ticket and $5 for each adult ticket adds up to $2725

We can use either the substitution method or elimination method to solve this. Let's use the elimination method. By multiplying Eq. I by 3, we can eliminate the "x" by subtracting Eq. II from Eq. I:

3(x + y = 621) multiply Eq. I by 3

3x + 3y = 1863 simplify

3x + 5y = 2725 Eq. II

0x - 2y = -862 result of subtraction

-2y = -862 simplified

y = -862/-2 divide both sides by -2 to isolate y

y = 431

Use Eq. I to solve for x:

x + y = 621 Eq. I

x + 431 = 621 substituting 431 for y

x = 621 - 431 subtract 431 from both sides to isolate x

x = 190

The number of child tickets sold is x, or 190.

The value of the adult tickets sold is 5y = 5(431) = 2155, or $2155.

Hope this helps!

Answer 2

This is simultaneous equations:

Write them:

c + a = 621, a = 621 - c

3c + 5a = 2725

Substitute:

3c + 5(621 - c) = 2725

Distribute:

3c + 3105 - 5c = 2725

Combine terms:

-2c = -380

Divide

c = 190 child tickets

621 - 190 = 431 adult tickets = a