Outdoor School Room Distribution

One hundred sixty-nine pupils were accommodated in 45 rooms at the outdoor school. Some were triple, and some quadruple, and all were fully occupied. How many were triple and quadruple rooms there?

Final Answer:

a =  11
b =  34

Step-by-step explanation:


45 = a + b
169 = 3a + 4b

45 = a + b
169 = 3·a + 4·b

a+b = 45
3a+4b = 169

Pivot: Row 1 ↔ Row 2
3a+4b = 169
a+b = 45

Row 2 - 1/3 · Row 1 → Row 2
3a+4b = 169
-0.33b = -11.33


b = -11.33333333/-0.33333333 = 34
a = 169-4b/3 = 169-4 · 34/3 = 11

a = 11
b = 34

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