Question

The sum of twice a number and a larger number is 145. The difference between the numbers is 55. Let x represent the smaller number and y represent the larger number. Which equations represent the situation? Check all that apply.

A. x-y=55
B. 2(x+y)=145
C. 2x+y=145
D. y-x=55
E. y=x+55

Answer 1

C, D, and E all represent parts of the situation.

A does not, because x is actually 55 smaller than y, which is why both D and E work.

B does not because it's doubling the sum of x = y, but the description says to double x and then add y (which is why C works).

Answer 2

x and y are the numbers
y>x

sum (addition) of twice a number (2x) and larger number (y) is (=) 145
2x+y=145

difference between them is 55 (y is bigger so it would be x is subtracted from y)
y-x=55

so the equations are

2x+y=145 and
y-x=55

we could add x to both sides in the 2nd equation to obtain
y=x+55, but that doesn't really represent that the difference is 55, though they are the same euation

so I would say C and D only