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vodka [1.7K]
3 years ago
11

Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. ho

w many liters of each does he need to make the needed 30 liters of 60% acid solution?
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
7 0

x = liters of 40% solution

y = liters of 70% solution

Gabe needs 30 liters, so

x + y = 30

Each liter of 40% solution contributes 0.4x liter of acid; each liter of 70% solution contributes 0.7y liter of acid. Gabe needs a solution with concentration 60%, which from 30 liters amounts to a net volume of 0.6*30 = 18 liters of acid. So

0.4x + 0.7y = 18

Solve the system however you like. By substitution, we have

y = 30 - x

0.4x + 0.7(30 - x) = 18

0.4x + 21 - 0.7x = 18

3 = 0.3x

==> x = 10 ==> y = 20

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<h3>Answer:  25w+200 > 750</h3>

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

Explanation:

He starts off with 200 cards. Then he adds on 25w more cards for each week (w). Overall, he'll have 200+25w cards

We can think of it like this:

  • After 1 week, he adds on 25*1 = 25 cards
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So that's another way to see where the 25w comes from.

The expression 200+25w is the same as 25w+200. This is because we can add two numbers in any order.

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Since he wants to know when he'll have more than 750 cards, this means we set 25w+200 greater than 750.

That's how we get to the answer of 25w+200 > 750

Notice how there isn't a line under the inequality sign. We aren't using the "greater than or equal to" symbol here. We want to know when the cards gets over 750, but we don't want to know when it's equal to 750.

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