Question

One-third of the number increased by 7 is equal to 5 less than one-fourth of that number. Find the number.

Answer 1

Hint: Assume that the number is x. Hence find the expression for one-third of the number increased by 7 and the expression for 5 less than one-fourth of the number. Equate the expressions and hence form an equation in x. Solve for x. Hence find the value of the number.

Complete step-by-step answer:

Let the number be x.
Hence, we have one -third of the number $=\dfrac{x}{3}$
Hence, we have one-third of the number increased by 7 $=\dfrac{x}{3}+7$
Also, we have one-fourth of the number $=\dfrac{x}{4}$
Hence, we have 5 less than one-fourth of the number $=\dfrac{x}{4}-5$
According to the question, one-third of the number increased by 7 is equal to 5 less than one-fourth of the number.
Hence, we have
$\dfrac{x}{3}+7=\dfrac{x}{4}-5$
Subtracting 7 from both sides, we get
$\dfrac{x}{3}=\dfrac{x}{4}-12$
Subtracting $\dfrac{x}{4}$ from both sides, we get
$\dfrac{x}{3}-\dfrac{x}{4}=-12$
Multiplying both sides, by 12, we get
$4x-3x=-144$
Hence, we have x = -144
Hence the number is -144.

Note: Verification:
One-third of -144 is equal to $\dfrac{1}{3}\left( -144 \right)=-48$
Hence one-third of -144 increased by 7 = -48+7 =-41
Also, one-fourth of -144 $=\dfrac{-144}{4}=-36$
Hence, 5 less than one-fourth of -144 =-36-5=-41
Hence one-third of -144 increased by 7 is equal to 5 less than one-fourth of the -144
Hence, our answer is verified to be correct.