Question

Manuel ate 1/3 of a crakers on a plate.hia brother ate 1/4 of the crakers.there were 5 crakers left on the plate.how many crakers were on the plate to begin with?

Answer 1

Given:

Manuel ate $\frac{1}{3}$ of the crackers on a plate

Her brother ate $\frac{1}{4}$ of the crackers

No. of crackers left on the plate = 5

To find:

No. of crackers on the plate at the beginning

Solution:

Let "x" be the total no. of crackers on the plate at the beginning

So,

No. of crackers Manuel ate = $\frac{x}{3}$

No. of crackers her brother ate = $\frac{x}{4}$

∴ No. of crackers left on the plate was,

= $x - \frac{x}{3} - \frac{x}{4}$

= $\frac{12x - 4x- 3x}{12}$

= $\frac{5x}{12}$

But, we are given 5 crackers left on the plate, so the eq. will be  

∴ $\frac{5x}{12}$ = 5

⇒ $x = \frac{5\:\times\:12}{5}$

⇒ $\bold{x = 12}$

Thus, there were 12 crackers on the plate, to begin with.

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