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BUY GIFT BACK OK

To a busy Singaporean, holidays are our favourite times of the year. And whether it’s a short trip to KL or a long getaway to Europe, there’s no escaping having to bring some gifts back for family, friends and half the office.

If we have a budget of $120 and 15 people to get gifts for, and we cannot decide between t-shirts and socks, how many of each should we get to maximise the budget? Assume that a t-shirt costs $8.40 and a pair of socks costs $5.60, and each person only receives either a t-shirt or a pair of socks.

Solution

We can find out the number of each gift to get by solving a pair of simultaneous equations.

Let the number of t-shirts be A, and the number of pairs of socks be B.
The total number must add up to 15 gifts.

So we have our first equation:

Equation 1

A + B = 15

The cost of all the gifts must add up to our budget, which is $120.
The total cost is the number of each gift, multiplied by their respective costs.

So we have our second equation:

Equation 2

A(8.40) + B(5.60) = 120

To solve these pair of equations, we can use the Substitution method. By changing the subject of one of the equations, and placing it into the second equation, we can find out the unknowns one at a time.

Changing the subject of Equation 1, we will get

Equation 3

A = 15 – B

We then substitute Equation 3 into Equation 2 to get

(15 – B)(8.40) + B(5.60) = 120
126 – 8.4B + 5.6B = 120
126 – 120 = 8.4B – 5.6B
6 = 2.8B
B = 62.8
B ≈ 2.14

Once we find B, we can find A by substituting it back into Equation 3.

So A = 15 – 2.14 = 12.86

Question: Since A and B are the numbers of gifts to get, they should be whole numbers. But they’re not. So do we round them up or down?

Because we have a fixed budget of $120, we should round the quantity of the more expensive item down. Since the t-shirt is more expensive than the socks, we round B up and A down.

So we’ll get B = 2.14 ≈ 3
And A = 12.86 ≈ 12

Thus, with our budget, we can get 12 t-shirts and 3 pairs of socks. Use this method to find out how to maximise your budgets when you go shopping!