Word Problem 15

Problem 15: A sum of 24 is divided into two parts so that seven times the first part added to five times the second part makes 146,

The value of the first part is ;

a. 13                   b. 11                   c. 17                     d. 7

Summation problems, math of summation —


Let the first part of the sum is ‘x’ and second part is ‘y’

\Rightarrow x+y=24 ---- (1))

Now by given information;

\Rightarrow 7x+5y=146 ---- (2)

To find value of first part i-e ‘x’ we eliminate ‘y’  by solving these two equations simulataneously;

Multiply eq 1 by 5 on both sides;

\Rightarrow 5x+5y=120 ---- (3)

Now subtracting eq 3 from eq 2;


\Rightarrow x=13

so, the first part of the sum is 13