Lindsay J. answered • 09/08/19
Tutor over multiple subjects, including Microsoft Office and GED
You first need to identify what your two equations are.
One will deal with cost and one will deal with quantity sold
b+ w= 766
b=Blueberry
w=Walnut
You can use x and y or any variables you want. I try to stick with something that relates back to the problem so that it is easy to remember.
Your second equation is:
10b + 12w =8360
You know this because the problem tells you that blueberry coffee cake is sold for $10 each and the walnut coffee cake is sold for $12 each.
Your two equations put together:
b + w= 766
10b + 12w =8360
With elimination you can manipulate the problem to make it work for you. Looking at both equations, you see that they are both positive, so you will have to make one equation a negative. Since the first equation is dealing with quantity you can easily change either the b or the w to the number you need it to be. I typically will go with a number like 5, 10, 20 etc. Just easier to do the math in your head.
-10(b + w=766)
-10b -10w =-7660 (new equation, you will use this one to solve your systems)
10b +12w=8360
Looking at the equations this way you can now see that your blueberry coffee cake can be eliminated, leaving you with the w to solve for first.
-10w+12w=2w
-7660+8360= 700
2w=700
You want to get the variable by itself so you want to divide both sides by 2.
w=350
Now that you have w, you can plug it back into the equation and solve for b. It is easier to use the original quantity equation so you don't have any extra steps
b+ w=766
(plug in 350 for w)
b+350=766
(get b by itself)
766-350=416
b=416
w=350
If you want to check to make sure this is correct, plug the numbers into the second equation
10(416) + 12(350)
4160+ 4200=8360
