Cinema costs
Weekly Problem 41 - 2009
At a cinema a child's ticket costs £4.20 and an adult's ticket costs £7.70. How much did is cost this group of adults and children to see a film?
At a cinema a child's ticket costs £4.20 and an adult's ticket costs £7.70. How much did is cost this group of adults and children to see a film?
Age
11 to 14
Challenge level
Problem
At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. When a group of adults and children went to see a film, the total cost was £$C$, where $C$ is a whole number greater than $90$ and less than $96$.
What is the value of $C$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: £91
Finding combinations which add up to whole numbers of pounds
$2\times70\text p+ 3\times20\text p$ is a whole number of pounds
$2$ adults $+$ $3$ children $= £15.40+ £12.60$
$= £28$
But $ £28\times3$ is less than $90$ and $28\times4$ is more than $100$
$10$ adults $= £77$
$5$ children $= £21$
$77+21=98$ too big
$21\times3 + 28 = 91$
$(3$ lots of $5$ children$) + (2$ adults $+ $ $3$ children$) = £91$
Using multiples of $70\text{p}$
Both $ £4.20$ and $ £7.70$ are multiples of $70p$, so $ £C$ must also be a multiple of $70p$. The only multiple of $70p$ between $ £90$ and $ £96$ which is a whole number of pounds is $ £91$.
$7$ children and $8$ adults cost:
$7\times £4.20+8\times £7.70= £29.40+ £61.60= £91$.
Or
$18$ children and $2$ adults cost:
$18\times £4.20 + 2\times £7.70 = £75.60 + £15.40 = £91$.