Question

A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-quarter of the second number and 5. The situation can be represented by using the graph below, where × represents the second number. 1.0 6 8 10 12 14 16 Which equations represent the situation?

Answer 1

Explanation:

There is no graph attached.

Convert the English phrases into expressions:

1. "A number (Let's call it x) is equal to the sum of half a second number (y) and 3"

x = (1/2)y + 3

2. "The first number (x) is also equal to the sum of one-quarter of the second number (y) and 5"

x = (1/4)y + 5

Let's rewrite these in standard form:

x = (1/2)y+3

2x = y + 6

y = 2x - 6

and

x = (1/4)y + 5

4x = y + 20

y = 4x - 20

A plot of these two lines is attached. Match them with the graph.