A problem with carrots...

Probability Level pending

A carrot farmer has sent an order of 70 kg of carrots to the markets in standard sized boxes. If he had used larger boxes, each capable of carrying 2 kg more, he would need 4 fewer boxes.

What is the capacity of the standard sized boxes, in kilograms?

10 14 5 2 7

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Jeremy Galvagni
Aug 13, 2018

The single equation that fits the given information is 70 x − 4 = 70 x + 2 \frac{70}{x}-4=\frac{70}{x+2}

Multiply all by x ( x + 2 ) x(x+2)

70 ( x + 2 ) − 4 x ( x + 2 ) = 70 x 70(x+2)-4x(x+2)=70x

− 4 x 2 − 8 x + 140 = 0 -4x^{2}-8x+140=0

x = 5 x=5 , or x = − 7 x=-7

So the box capacity is 5 \boxed{5} .

Checking: 70 5 = 17 \frac{70}{5}=17 , but 70 7 = 10 \frac{70}{7}=10 which is 4 fewer.

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