# Question

Benny bought 120 t-shirts and shorts in total for a sports camp. The price of a t-shirt is \$12.50 and the price of a pair of shorts is \$11. The price of all the t-shirts is \$301.50 more than the price of all the shorts.

a) How many pairs of shorts did Benny buy?

b) How much did he spend altogether?

Source: .

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https://www.kiasuparents.com/kiasu/question/79669-2/

If you want to let your kid practice Guess-and-Check, can try below. Total Qty is 120. As kids progress with more complex methods, they may drop the “troublesome” Guess-and-Check method but it is still a good thing to practice once in a while until the big PSLE.  Can also consider a little hybrid by making supposition (for every exchange) to save some time on guess and check. Still three sets of checking in below table.

 \$ per T-shirt Qty of T-shirts Total \$ T-shirts \$ per shorts Qty of shorts Total \$ Shorts Diff \$12.50 let’s take 60 \$750 \$11 60 \$660 \$90 suppose 61 \$762.50 59 \$649 \$113.50 *see note *see note *see note 69 \$862.50 51 \$561 \$301.50 ok

*analyse and deduce that for every one set of exchange from 1 pair of shorts to 1 T-shirt, Benny is spending \$113.50-\$90 = \$23.50 more on T-shirts.  (Or save \$11 + spend \$12.50 = \$23.50 more on T-shirts)

\$301.50 – \$113.50 = \$188.00

\$188.00 / \$23.50 = 8 more exchanges (–> 59-8 = 51 pairs of shorts) (–> 61+8 = 69 T-shirts).

Put back into table and check*

(a) 51 pairs of shorts#

(b) \$862.50 + \$561= \$1423.50#

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These questions are quantity/value questions.  Common variations of the quantity/value within the question include animals / no. of legs, vehicles / no. of wheels, item / cost etc. The assumption method is just one way of solving it.

I prefer the table method below:

 Item Quantity Value Total value (Quantity x Value) T-shirt 1 unit \$12.50 \$ (12.50 units) Shorts 120 – 1 unit \$11 \$ (1,320 – 11 units)

a) 12.50 units = 1,320 – 11 units + 301.50
23.5 units = 1,621.5
1 unit = 69 T-shirts

120 – 69 = 51 pair of shorts

b) 69 x \$12.50 = \$862.50
51 x \$11 = \$561

\$862.50 + \$561 = \$1423.50

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