SOLUTION: On Monday Luis picked up seven scones and two large coffees for the office staff. He paid $22.80. On Tuesday, Rachel picked up four scones and three large coffees for the office st

Question 1196487: On Monday Luis picked up seven scones and two large coffees for the office staff. He paid $22.80. On Tuesday, Rachel picked up four scones and three large coffees for the office staff. She paid $16.52. What is the cost of one scones? What is the cost of one large coffee?
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = cost of 1 scone
y = cost of 1 coffee
Prices are in dollars

7x = cost of 7 scones
2y = cost of 2 coffees
7x+2y = total cost
7x+2y = 22.80

Follow similar steps to get the other equation of 4x+3y = 16.52

We have this system of equations
7x+2y = 22.80
4x+3y = 16.52

Let's say we wanted to eliminate the y terms
Triple both sides of equation (1) and double both sides of equation (2)
We'll end up with this equivalent system
21x+6y = 68.40
8x+6y = 33.04
The goal is to have the y terms match (ie both coefficients are 6)

Now subtract straight down
The x terms subtract to 21x-8x = 13x
The y terms subtract to 6y-6y = 0y = 0, so they cancel out.
The right hand sides subtract to 68.40-33.04 = 35.36
After the y terms cancel, we have: 13x = 13.56
That solves to x = 2.72 after dividing both sides by 13

Let's find the value of y based on that x value
Pick any previously mentioned equation involving x and y
Plug in x = 2.72 and solve for y
7x+2y = 22.80
7(2.72)+2y = 22.80
19.04+2y = 22.80
2y = 22.80-19.04
2y = 3.76
y = 3.76/2
y = 1.88

Answer:
Price of one scone = $2.72
Price of one coffee = $1.88

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Prices c for the coffee, n for the scone

LUIS:

RACHEL:

Solve those as a system.

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