The diagrams show the price paid by two groups of people visiting a funfair - OCR - GCSE Maths - Question 8 - 2019 - Paper 4

To eliminate one variable, we can multiply the first equation by 3 and the second equation by 5 to align the coefficients of 'a':

1. Multiply the first equation by 3:
   $15a + 12c = 234$

2. Multiply the second equation by 5:
   $15a + 30c = 315$

Now, we subtract the first modified equation from the second modified equation:

$(15a + 30c) - (15a + 12c) = 315 - 234$

This simplifies to:

$18c = 81$

Thus, by dividing both sides by 18, we find:

$c = 4.5$

Now that we have the price of a child, we can substitute 'c' back into one of our original equations to find 'a'. Using the first equation:

$5a + 4(4.5) = 78$

This simplifies to:

$5a + 18 = 78$

Subtracting 18 from both sides gives:

$5a = 60$

Finally, dividing both sides by 5 yields:

$a = 12$

Therefore, the price for an adult is £12 and the price for a child is £4.50.