Let the number of t-shirts be A, and the number of pairs of socks be B.So we have our first equation:
The total number must add up to 15 gifts.
The cost of all the gifts must add up to our budget, which is $120.So we have our second equation:
The total cost is the number of each gift, multiplied by their respective costs.
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
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!