Question 89688: A donut shop sells a box of 7 cream-filled and 5 jelly donuts for $6.32, and a box of 4 cream filled and 8 jelly donuts for $6.08. Find the cost of a single cream filled and a single jelly donut".
I know it's 2 variables and 2 equations. I have it set up like this
7x + 5y = 6.32
4x + 8y = 6.08
I was thinking to get rid of the decimals by mult by 100. I need some help please and maybe step by step instructions. Thank you so much
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1st: 7x + 5y = 6.32
2nd: 4x + 8y = 6.08
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Multiply 1st by 4 and 2nd by 7 to get:
3rd: 28x + 20y = 4*6.32
4th: 28x + 56y = 7*6.08
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Substract 3rd from 4th and solve for y:
36y = 7*6.08-4*6.32
y = 0.48
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Substitute in 7x+5y=6.32 to solve for x
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I'll leave the rest to you but x=0.56
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Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! 7x + 5y = 6.32
4x + 8y = 6.08
Multiply both sides 100
100(7x + 5y) =100* 6.32
100(4x + 8y) =100* 6.08
Distribute and multiply
700x+500y=632
400x+800y=608
Now lets use elimination to solve for x and y
| Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition |
Lets start with the given system of linear equations
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).
So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.
So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 700 and 400 to some equal number, we could try to get them to the LCM.
Since the LCM of 700 and 400 is 2800, we need to multiply both sides of the top equation by 4 and multiply both sides of the bottom equation by -7 like this:
 Multiply the top equation (both sides) by 4
 Multiply the bottom equation (both sides) by -7
So after multiplying we get this:
Notice how 2800 and -2800 add to zero (ie  )
Now add the equations together. In order to add 2 equations, group like terms and combine them
 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.
So after adding and canceling out the x terms we're left with:
 Divide both sides by  to solve for y
 Reduce
Now plug this answer into the top equation to solve for x
 Plug in
 Multiply
 Reduce
 Subtract  from both sides
 Combine the terms on the right side
 Multiply both sides by  . This will cancel out  on the left side.
 Multiply the terms on the right side
So our answer is
,
which also looks like
( ,  )
Notice if we graph the equations (if you need help with graphing, check out this solver)
we get
 graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).
and we can see that the two equations intersect at (,). This verifies our answer. |
Since this means  (just convert to decimal form). So the price of a cream filled donut is $0.56 or 56 cents
Since this means  (just convert to decimal form). So the price of a jelly donut is $0.48 or 48 cents
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