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: (x + y = 10)
Equation 2: (y = 4x)
a) Equation 1
b) Equation 2
c) Both
d) None of the above

Answer 1

Both Equation 1 (x + y = 10) and Equation 2 (y = 4x) are needed to represent the system for the problem where the sum of two numbers is 10 and the larger number is 4 times the smaller number.

Step-by-step explanation:

To solve the problem where the sum of two numbers is 10, and the larger number is 4 times the smaller number, we use a system of linear equations. By letting x represent the smaller number and y represent the larger number, we can frame the problem using two equations. Equation 1 is x + y = 10, which expresses the information that the sum of the two numbers is 10. Equation 2 is y = 4x, which tells us that the larger number, y, is four times the smaller number, x. Therefore, the answer to the student's question is c) Both, meaning both Equation 1 and Equation 2 are needed to correctly represent the system for this word problem.