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Kitty [74]
3 years ago
14

Sharon wants to know the difference between the average amount she stacked and the average amount Diane stacked. Which operation

would she use to find the difference?
Mathematics
1 answer:
jek_recluse [69]3 years ago
3 0
Sharon would subtract the amount that she stacked from Diane to figure out the difference.

Hope this helped :D
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Answers:

Gabe needs 30 liters of the 50% solution

Gabe needs 30 liters of the 70% solution

Both answers are 30

==================================

Explanation:

We have two beakers, each of which we don't know how much is inside. Let's call this x and y

x = amount of liquid in the first beaker (water+acid)

y = amount of liquid in the second beaker (water+acid)

We're told that the beakers have a 50% solution and a 70% solution of acid. This means that the first beaker has 0.5*x liters of pure acid, and the second beaker has 0.7*y liters of pure acid. In total, there is 0.5x+0.7y liters of pure acid when we combine the two beakers. This is out of x+y = 60 liters total, which we can solve for y to get y = 60-x. We will use y = 60-x later on when it comes to the substitution step

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(0.5x+0.7y)/(x+y) = (0.5x+0.7y)/60

We want this to be equal to 0.6 because Gabe wants a 60% solution when everything is said and done, so

(0.5x+0.7y)/60 = 0.60

0.5x+0.7y = 0.60*60 .... multiply both sides by 60

0.5x+0.7y = 36

0.5x+0.7( y ) = 36

0.5x+0.7(60-x) = 36 ........ replace y with 60-x (substitution step)

0.5x+0.7(60)+0.7(-x) = 36 .... distribute

0.5x+42-0.7x = 36

-0.2x+42 = 36

-0.2x = 36-42 .... subtract 42 from both sides

-0.2x = -6

x = -6/(-0.2) .... divide both sides by -0.2

x = 30

He needs 30 liters of the 50% solution

Use this x value to find y

y = 60-x

y = 60-30

y = 30

So he needs 30 liters of the 70% solution


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