Question 842757: Mixture Word problem
Mix together M&Ms and trail mix. The M&Ms are $7.00 per pound. And Trail Mix is $15.00 per pound. How many of each to get 480 pounds that would cost to be $8.00 per pound?
My 2 equations that I came up with are:
x+y=480
.7x+.15y=.8*480
so I did the subsitution method to solve. I solved the first problem as
Y=-x+480.
then my second equation came out to be .7x+.15y=384
Then I subsituted the first equation into the second equation and got
.7x +.15(-x+480)=384... I distributed the .15 to the -x and 480. The new equation came to be...
.7x-.15x+72=384.
then I combined the x's. subtracted 72 from both sides and got:
.55x=312
Then divided .55 to get x by it self, there for x=567.27
I know from here i would put the x= value into the first problem of x+y=480 But I know x is wrong... did i set it up wrong?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you are multiplying x by .7 when you should be multiplying x by 7.
same with y and same with 480.
.7 is 70 cents a pound.
you want 7 dollars a pound which is 7.
when you solved for y, you got y = x + 480.
that should have been y = 480 - x.
let me go through it and you'll see what and where you went wrong.
x + y = 480 is the first equation
7x + 15y = 8(480) is the second equation.
you want to solve by substitution.
start with x + y = 480
subtract x from both sides of this equation to get y = 480 - x
substitute for y in the second equation to get:
7x + (15 * (480 - x)) = (8 * 480)
simplify to get:
7x + (15 * 480) - (15 * x) = (8 * 480)
simplify further to get:
7x + 7200 - 15x = 3840
combine like terms to get"
-8x + 7200 = 3840
subtract 7200 from both sides of this equation to get:
-8x = 3840 - 7200
simplify to get:
-8x = -3360
multiply both sides of this equation by -1 to get:
8x = 3360
divide both sides of this equation by 8 to get:
x = 420
replace x in the equation of x + y = 480 to get 420 + y = 480
subtract 420 from both sides of this equation to get y = 480 - 420 which simplifies to y = 60
you have x = 420 and y = 60
7 * 420 + 15 * 60 = 3840 for 480 pounds of mix.
divide 3840 by 480 to get:
cost per pound for the mix is equal to 8.
numbers check out so the solution is good.
two mistakes that were obvious were:
you used .7 and .8 and .15 rather than 7 and 8 and 15.
you said y = x + 480 when you should have said y = 480 - x
i didn't check the rest out but, if you follow my logic, you should be able to see where else you went wrong, if you did anything else wrong.
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