solving systems by elimination multiply (solve and show work please)

Question

Jamian bought a total of 40 bagels and donuts for a morning meeting. 

1. He paid a total of $33.50. 
2. Each donut cost $0.65. 
3. Each bagel cost $1.15. 

Let x represent the number of bagels and let y represent the number of donuts. 

Answer 1

Hi Melanie

You have 15 Bagels and 25 Donuts please see below

Equation 1 is for the total number of items 40

x + y = 40

Note here that y = 40 - x

Equation 2 is for the cost per item and the total cost

1.15x + 0.65y = 33.50

If we multiply Equation 1 by negative 0.65 we can eliminate y

Equation 1 becomes

-0.65x - 0.65y = -26

Combine the adjusted Equation 1 with Equation 2 then y is eliminated and we are left with

-0.65x - 0.65y = -26

1.15x + 0.65y = 33.50

0.5x = 7.50

Divide both sides by 0.5 to solve for x

x = 15

y = 25 ( because y = 40 - x = 40 - 15 = 25)

Checking in Equation 2

1.15(15) + 0.65(25) = 33.50

17.25 + 16.25 =33.50

33.50 = 33.50

Hope this helps