Question

10. The difference between two positive integers is 40 and their ratio is 1:3.
(a) Form x and y equation for the two numbers.​

Answer 1

ANSWER:

• The two equations are x - y = 40 and x - 3y = 0.

GIVEN:

• The difference between two positive integers is 40 and their ratio is 1:3.

TO FORM:

• x and y equations for the two numbers.

EXPLANATION:

Let the greater number be x and the smaller number be y.

=> x - y = 40

=> y : x = 1 : 3

=> y/x = 1/3

=> x = 3y

=> x - 3y = 0

Hence the two equations are x - y = 40 and x - 3y = 0.

SOLUTION:

=> x - y = 40

Substitute x = 3y.

=> 3y - y = 40

=> 2y = 40

=> y = 20

Substitute y = 20 in x - y = 40.

=> x - 20 = 40

=> x = 60

VERIFICATION:

=> x - y = 40

Substitute y = 20 and x = 60.

=> 60 - 20 = 40

=> 40 = 40

Substitute y = 20 and x = 60.

=> y : x = 1 : 3

=> 60 : 20 = 1 : 3

=> 1 : 3 = 1 : 3

HENCE VERIFIED.