Could you please show me the steps to working this out?

Question

The local show has two entry/ ride options. The first option is $10 entry then $2.50 per ride. The second
option is $5 then $3.50 per ride. Use an equation to help work out how many rides you need so that both
options cost the same.

Answer 1

$10 + $2.50*X = $5 + $3.50*X

 

10 + 2.50X = 5 + 3.50X  <--- factors out $1, and the dollar signs cancel out for readability

 

100 + 25X = 50 + 35X <--- multiplies everything by 10 to clear away the decimals

 

0 = 50 + 35x - 100 - 25x <--- everybody to the right side so leading coefficient stays positive

 

0 = 10x - 50 <-- combines like terms

 

50 = 10x   <--- adds 50 to both sides; 50 goes to the left side

 

x = 50/10 = 5

 

CHECK:

  10 + 2.50*5 = 10 + 12.50 = 22.50

 

       vs

 

 5 + 3.50*5 = 5 + 17.50 = 22.50

 

Yes, ma'am, the answer is 5