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hidalgo8429
14.12.2020 •
Mathematics
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Ответ:
Answers:
x = 2.40
y = 1.60
This means 1 hot cocoa costs $2.40 and 1 pretzel costs $1.60
=======================================
Work Shown:
x = cost of 1 cup of hot cocoa
y = cost of 1 pretzel
5x = cost of 5 cocoas
4y = cost of 4 pretzels
5x+4y = cost of 5 cocoas+4 pretzels
5x+4y = 18.40
----------------
2x = cost of 2 cocoas
4y = cost of 4 pretzels
2x+4y = cost of 2 cocoas+4 pretzels
2x+4y = 11.20
----------------
The system of equations we have is
Note how 4y shows up twice. This is handy to be able to get rid of the y terms completely.
How? By subtracting the equations straight down
The x terms subtract to 5x-2x = 3x
The y terms subtract to 4y-4y = 0y = 0 and they go away
The right hand sides subtract to 18.40 - 11.20 = 7.20
After those three separate subtractions, we have this new equation:
3x = 7.20
Divide both sides by 3 to isolate x
3x/3 = 7.20/3
x = 2.40
Each hot cocoa costs $2.40
Now use this x value to find y. You can pick any equation you want as long as it has x,y in it. I'll pick the first equation
5x+4y = 18.40
5(2.40)+4y = 18.40
12+4y = 18.40
4y = 18.40-12
4y = 6.40
y = 6.40/4
y = 1.60
Each pretzel costs $1.60
If we picked on the second equation, we should get the same y value
Let's find out
2x+4y = 11.20
2(2.40)+4y = 11.20
4.80+4y = 11.20
4y = 11.20-4.80
4y = 6.40
y = 6.40/4
y = 1.60
We get the same result as before.
To check the answers, you need to plug those values back into the two original equations and simplify. You should get the same thing on both sides.