Quadruple 7654

Triple and quadruple rooms are available in the cottage for 30 children. Rooms are occupied so that all beds are always occupied. Determine how many rooms the children will occupy in total if there are four times as many children in the four-bedroom rooms as in the three-bedroom.

Correct answer:

p =  8

Step-by-step explanation:


30 = 3a+4b
4b = 4·(3a)
p=a+b

30 = 3·a+4·b
4·b = 4·(3·a)
p=a+b

3a+4b = 30
12a-4b = 0
a+b-p = 0

Pivot: Row 1 ↔ Row 2
12a-4b = 0
3a+4b = 30
a+b-p = 0

Row 2 - 3/12 · Row 1 → Row 2
12a-4b = 0
5b = 30
a+b-p = 0

Row 3 - 1/12 · Row 1 → Row 3
12a-4b = 0
5b = 30
1.333b-p = 0

Row 3 - 1.33333333/5 · Row 2 → Row 3
12a-4b = 0
5b = 30
-p = -8


p = -8/-1 = 8
b = 30/5 = 6
a = 0+4b/12 = 0+4 · 6/12 = 2

a = 2
b = 6
p = 8

Our linear equations calculator calculates it.



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