Question

The sum of two numbers is 18. Three times the greater number exceeds four times the smaller number by 5. Find the numbers

Answer 1

6 1/8 and 11 7/8

Explanation:

Just use algebra. x+y is equal to 18. 3x=4y+5. Then you substitute the value x for y by dividing by three. From there it is just computation

Answer 2

The numbers are 11 and 7

Explanation:

Let the numbers be P and V

Let P be the greater number and V be the smaller number.

From the question, the sum of the numbers equals 18 i.e

P + V = 18

Also from the question,

We were told that three times the greater number exceeds four times the smaller number by 5 i.e

3P = 4V + 5

P = (4V + 5) / 3

Substituting the value of P into equation (1), we obtain:

P + V = 18.

(4V + 5) / 3 + V = 18

Multiply through by 3 to express in linear form, we have:

4V + 5 + 3V = 54

Collect like terms

4V + 3V = 54 - 5

7V = 49

Divide both side by the coefficient of V i.e 7

V = 49/7

V = 7

P + V = 18

P = 18 - V

P = 18 - 7

P = 11

The numbers are 11 and 7