I need help with this math problem?

Question

Stella's catering is planning a wedding reception. The bride and the groom would like to serve a nut mixture containing 25% peanuts. Stella has available mixtures that are either 40% peanuts or 10% peanuts. How much of each type should be mixed to get a 10lb mixture of peanuts?
Im supposed to use system of equations but idk how to put it together... Can someone smarter than me help me? I appreciate it.

U GUYS R SO MUCH SMARTER THAN ME! Thank you!

Answer 1

First, you have the equation for the total mix ..

10 = x + y .......... (x is the amount of the 40% mix and y is the amount of the 10% mix).

Now for the combination, you need ...

.25 (x + y) = .4x + .1y

This equation says that 25% of the amount of x and y combined must be peanuts (the left side). To get that, you have to combine the x amount (that is 40% peanuts) plus the y amount that is 10% peanuts).

So now you have two equations to solve.

10 = x + y .... and .... .25x + .25y = .4x + .1y ... I distributed.

The easiest way to solve this would be substitution. Before I do it, however, I want to manipulate both equations some.

10 - y = x .... I get x alone so it is substitution ready.

-.15x = -.15y ... I moved/combine terms to make it easier to use.

so now put (10 - y) in for x

-.15(10 - y) = -.15y ... time to distribute again ...

-1.5 + .15y = -.15y ... get the y's on one side and the #'s on the other.

-1.5 = -.3y ... divide both sides by -.3 to get y alone ...

5 = y ... that means you need 5 pounds of y (the 10% mix).

If you want a total of 10 pounds, then that means you need 5 pounds of x (the 40% mix).

You have solved with a system of equations using substitutions, which is what I am guessing your teacher would like to see.

Answer 2

stella wants 10 lb mixture containing 25% peanuts so she needs 25% 0f 10 lbs peanuts,
25 / 100 * 10 = 2.5 lbs.
let's say she takes x lbs of mixture A
to get 10 lbs total, she will need to take (10 - x ) lbs of mixture B.
peanuts from mixture A (40%) = 40% of x = 40 / 100 * x
= 2x/5 lbs
peanuts from mixture B(10%) = 10 % of (10 - x)
= 10/100 *(10-x) = (10 - x ) /10 lbs
total peanuts = 2x / 5 + (10 - x ) / 10
= 2.5 lbs
so the equation is 2x/5 + (10-x)/10 = 2.5
taking the LCM as 10
(4x + 10 - x ) / 10 = 2.5
cross multiplying
3x + 10 = 25
3x = 15
x = 5
so 5 lbs of mixture A and 5 lbs of mixture B.

checking,
from 5 lbs of mixture A : 40% of 5 lbs = 2 lbs
from 5 lbs of mixture B : 10% of 5 lbs = 0.5 lbs
total peanuts = 2.5 lbs out of a total of 10 lbs which gives us the required 25% as per the question.

Answer 3

Let us assume that she mixes x lb of40% nut mixture and 10-x lb of 10% nut mixture to get 10 lb of 25% nut mixture.Hence,according to the problem... x(40/100) +(10-x)(10/100) = 10(25/100) Multiplying all the terms by 100,we get 40x+10(10-x)=10*25 => 40x+100-10x=250 =>30x=250-100=150 =>x=150/30=5 Therefore she should mix 5 ln of 40% with (10-5 or) 5 lb of 10% of nut mixture.

Answer 4

10 lbs * 0.25 = 2.5 lbs

x * 0.1 + (10 - x) * 0.4 = 2.5 lbs = 4 - 0.3 x
0.3x = 1.5 lbs
x = 5.

5 lbs of 10 % + 5 lbs of 40 %