sell at either 50c or $1 each. sold 229, collected $140 in total. the number sold at 50c be X and the number sold at $1 be Y. explain why x+2y=280

Question

 10 math 

Answer 1

Hi Hayley-Louise,

 

X is the number of items sold at $0.50 each.

Y is the number of items sold at $1 each.

You know that you made $140 altogether.

 

So, the equation that describes how you made this money is

 

0.50X + 1Y = 140

 

You are always free to multiply both sides of any equation with whatever number you wish. Since you are multiplying both sides of the equation with the same number, you still keep the balance of the equation. So, let's multiply both sides of the above equation by 2.

 

2(0.50X + 1Y) = (2)(140)

 

This becomes

 

(2)(0.50X) + (2)(1Y) = 280

 

Or

 

X + 2Y = 280

 

which is what you are asking about.