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Word Problems with Two Unknowns

≈ 30 min
0/3 practice checks

Two unknown quantities → define two variables → hunt the story for two independent facts.

Worked example. At the school fundraiser, 2 pies and 3 cooldrinks cost R59; 1 pie and 2 cooldrinks cost R34. Find the price of a pie.

Let pp = pie price, dd = cooldrink price (in rand):

2p+3d=59(1)2p + 3d = 59 \qquad (1)
p+2d=34(2)p + 2d = 34 \qquad (2)

From (2): p=34−2dp = 34 - 2d. Substitute into (1):

2(34−2d)+3d=59  ⇒  68−d=59  ⇒  d=92(34 - 2d) + 3d = 59 \;\Rightarrow\; 68 - d = 59 \;\Rightarrow\; d = 9

Then p=34−18=16p = 34 - 18 = 16. A pie costs R16 (and a cooldrink R9). Check in (1): 32+27=5932 + 27 = 59 ✓

2 pies and 3 cooldrinks cost R59; 1 pie and 2 cooldrinks cost R34. What does one pie cost, in rand?

At a soccer match, 2 adult tickets and 3 child tickets cost R330; 1 adult and 1 child ticket cost R140. What does one child ticket cost, in rand?

Two numbers have a sum of 30 and a difference of 8. Which system describes this?