childs tickets are 5 dollars adult tickets are 8 dollars how many ticket were sold if there was 550 dollars at the end of the day

Question

A museum sold adults and child tickets for an upcoming event. There were 10 more child tickets sold than adult tickets. Child tickets cost $5, and adult tickets cost $8. The sales totaled $550. How many adult tickets were sold

Answer 1

5c+8a =550

$5 per child ticket

$8 per adult ticket

$550 = total ticket sales

10 more child tickets sold than adut tickets

c=10+a

5(10+a) + 8a = 550

50+5a +8a =550

5a+8a =550-50 = 500

13a = 500

a=500/13 = about 38.46 adult tickets

c= about 48.46 child tickets

5(48+ 8(39)=240+312= 552

5(49)+8(38)=245+304= 549

there's a problem in the problem, maybe miscopied or misprinted

but as given, 38 adult tickets and 49 child tickets comes closest to $550 total

IF the typo was 5 instead of 6, then

6c+8a=550

and

3c+4a=275

3(10+a)+8a=27

a =35 adult tickets

c= 45 child tickets

check the answers

6(45)+8(35)

=270+280=550

it works

or number of adult tickets = 500/13 which is not an integer

then 10 more chlld ticekts = 10+500/13 = 630/13

5(630/13)+8(500/13)

= 3150/13+4000/13

=7150/13 = 550

that's about 38 1/2 adult tickets and 48 1/2 child tickets