Question

The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?

Let x = the smaller number.

Let y = the larger number.

Which two equations represent the system for this word problem?

Equation 1:
Equation 2:

Answer 1

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Answer 2

SOLUTION

GIVEN

The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?

Let x = the smaller number.

Let y = the larger number.

TO DETERMINE

The two equations represent the system for this word problem

EVALUATION

Let x = the smaller number.

Let y = the larger number.

It is given that The sum of two numbers is 10

$\therefore \sf{ \: x + y = 10 \: \: \: .....(1)}$

Again it is also stated that The larger number is 4 times the smaller number

$\therefore \sf{ \: y = 4x \: \: \: .....(2)}$

So the required two equations are

$\sf{ \: x + y = 10 \: \: \: .....(1)}$

$\sf{ \: y = 4x \: \: \: .....(2)}$

From Equation (1) & Equation (2) we get

$\therefore \sf{ \: 5x = 10\: }$

$\therefore \sf{ \: x = 2\: }$

From Equation (2) we get

$\therefore \sf{ \: y = 4 \times 2 = 8\: }$

Hence the required two numbers are 2 & 8

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