Question

Need help with systems of equations word problem!
The research department of a company that manufactures children's fruit drinks is experimenting with a new flavor. a 17.5% fructose solution is needed but only 10%and 20% solutions are available. How many gallons of the 10% fructose solution should be mixed with the 20% fructose solution to obtain 20 gallons of 17.5% fructose solution?

I know how to solve a systems of equations problem, but I've really struggled to make the word problems into the equations themselves.

Answer 1

@mathstudent55 when you're not busy, could you help me?

Answer 2

@myininaya

Answer 3

@Owlcoffee

Answer 4

yo I got u

Answer 5

Thank you so much already XD

Answer 6

I hope

Answer 7

I'll help you out, this is a long one so I'll try to explain the problem as best as i can ;)

Answer 8

Let the amount of 20% solution be x gallons

Amount of 10% solution = 20 - x gallons

0.20 ( x) + 0.10 ( 20 - x) = 0.175 ( 20)

0.20x + 2 - 0.10x = 3.5

0.10x = 1.5
x = 1.5 / 0.10 = 15 gallons

ANSWER = 15 gallons ( 20%) 5 gallons ( 10%)
CHECK
0.20 ( 15) = 3
0.10 ( 5) = 0.5
Total 3.5 /20 X 100 = 17.5%

Answer 9

eziest way to do this is make a table

Answer 10

or listen to @MajesticGalaxy lel

Answer 11

your answer would be 17.5%

Answer 12

if you're speaking of matrices my math teacher decided to skip that...

Answer 13

nah. Just a 3 by 3 table

Answer 14

isn't there supposed to be another variable?

Answer 15

nvm

Answer 16

hang on.

Answer 17

No i do not think so

Answer 18

No, I know this wants me to do it a specific way, it's all about systems of equations

Answer 19

ok, so one of the equations is 0.1x+0.2y=20*0.175

Answer 20

the other I think is x+y=20

Answer 21

y being the 20% fructose?

Answer 22

yes.

Answer 23

THANK YOU

Answer 24

No prob, make sure u check if it makes sense!

Answer 25

I'll solve and see what I get

Answer 26

I'll try 2

Answer 27

K, I got x=5, y=15

Answer 28

I got that too! And it makes sense! Thank you so very much!

Answer 29

no prob!

Answer 30

If you look at @MajesticGalaxy 's solution, you will see that he is very close to the system of equations you need. He skipped defining variable y, and used substitution.

Below is a copy of his solution.
I will add what you need to have a system of solutions in between lines of *******.

Let the amount of 20% solution be x gallons

*********************************
Amount of 10% solution is y
You need a total of 20 gallons, so
x + y = 20
Solving for y, the amount of 10% solution, you get
*********************************

Amount of 10% solution = y = 20 - x gallons

**********************************
The amount of fructose is
0.20x + 0.10y = 0.175 * 20

Since we know that y = 20 - x, we substitute to get:
**********************************

0.20 ( x) + 0.10 ( 20 - x) = 0.175 ( 20)

0.20x + 2 - 0.10x = 3.5

0.10x = 1.5

x = 1.5 / 0.10 = 15 gallons

ANSWER = 15 gallons ( 20%)
5 gallons ( 10%)

CHECK
0.20 ( 15) = 3
0.10 ( 5) = 0.5
Total 3.5 /20 X 100 = 17.5%