Question

A group of 3 adults and 10 children bought tickets to watch a dance performance. Each adult ticket cost $7 more than each child ticket. The group paid a total of $125. What was the cost of each child ticket?​

Answer 1

Explanation:

So 3a + 10c = 125 is translation of first sentence. Second part says a = c+7, "more than" indicating addition.

Substitute the 1st equation's a with c+7

So 3(c+7) + 10c = 125

Distribute.*+

3c + 21 +10c = 125

*Remember that 3(c+7) means to add up

c+ 7

c + 7

c + 7

‐-----------------

3c + 21

Combine 3c + 10c as 13c

So 13c + 21 = 125. Subtract 21 on each side (always treat left and right sides equally, believe in equality for all!!)

13c = 104. Divide each side by 13 (opposite of x)

c = 8........this is cost of each children's ticket

($8). Check: adult ticket is c +7 or $15. Does 3 adult tickets x $15 + 10 child tickets × 8 = 125? 45. + 80 = 125

Ssolution is correct. Can also be graphically to see where 3x + 10y = 125 crosses line x = y + 7

x being cost adult and y being cost of kids ticket, look at y (kids price) of point of intersection