Question

A shop sells 3 T-shirts and 2 shorts for $9.20. It also sells 4 T-shirts
and 5 shorts for $18.10. James spent $348 on a number of shorts and
T-shirts in the ratio of 3:5 respectively.
(a) Find the cost of one shorts.
(b) How many shorts did James buy?

Answer 1

3t+2s = 9.20
4t+5s = 18.10
solve for t and s as usual. Then use those values in
t*3x + s*5x = 348
solve for x
he bought 3x shorts

Answer 2

3t + 2s = 920
4t + 5s = 1810

1st times 4 ---> 12t + 8s = 3680
2nd times 3 ---> 12t + 15s = 5430
subtract them:
7s = 1750
s = 250
then subbing back, t = 140

A t-shirt costs $1.40, and shorts cost $2.50

James shorts and t-shiprts in ratio of 3:5 or 3x : 5x
3x(250) + 5x(140) = 34800
1450x = 34800
x = 24

so he bought 3(24) shorts and 5(24) t-hirts
= 72 shorts, 120 t-shirts

check:
72(250) + 120(140) = 34800 , looks good