How to solve Maths Problem without algebra way. Primary School Question

Question

Caroline bought a school bag, a pair of shoes and a jacket for her son. She paid a total of $\$170$. The pair of shoes cost $\$23$ more than the school and $\$16$ less than the jacket How much did Caroline pay for the jacket?

Answer 1

Since the (idiotic, in my view) Singapore system wants you to avoid algebra (by which they seem to mean letters representing variables), draw a block to represent a school bag, the cheapest item. The shoes are a block plus $23$ dollars. The jacket is a block plus $23+16 = 39$ dollars.

The sum of all the three items is $170$. If you clip away the excess of $39$ and $23$ from the two more expensive items, you get three blocks. Three blocks will add up to $170 - 39 - 23 = 108$. One block will be $36$. That's the price of the school bag. So the price of the jacket is $39$ more, or $75$ dollars. Done.

Answer 2

Imagine you are about to pay for the three items. The cashier says it's 170. Then you say: I changed my mind, instead of the school bag I'll take another pair of shoes. Then the cashier says: it's 23 more for a total of 193. Then you change your mind again: instead of the jacket I'll take another pair of shoes. The cashier says: Then it's 16 less, the total is now 177 for three pairs of shoes. Now you know that each pair of shoes is 177/3=59, so the school bag is 59-23=36 and the jacket is 59+16=75.