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3 years ago

-5+1/5a=4 solution again.

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

6 0

Isolate the a. Note the equal sign. What you do to one side, you do to the other.

Add 5 to both sides

-5 (+5) + 1/5a = 4 (+5)

1/5a = 9

Isolate the a. Multiply 5 to both sides

(5)(1/5)a = 9(5)

a = 9 x 5

a = 45

45 is your answer for a.

hope this helps

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Read 2 more answers

Mary wants to make 20 gallons of a 52% acid solution by mixing together a 84% acid solution and a 4% acid solution. How much of

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Answer:

12 gallons 84%
8 gallons 4%

Step-by-step explanation:

I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.

Here, that means the ratio of 84% solution to 4% solution is ...

48 : 32 = 12 : 8

Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)

Mary must use ...

12 gallons of 84% acid solution
8 gallons of 4% acid solution

You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.

_____

<em>Check</em>

12 × 84% + 8 × 4% = 10.40 = 20 × 52%

_____

<em>Usual Solution</em>

A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...

0.84x + 0.04(20 -x) = 0.52(20)

0.80x + 0.8 = 10.4 . . . . simplify

0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8

x = 9.6/0.8 = 12 . . . . gallons of 84% acid

20-x = 8 . . . . . . . . . . gallons of 4% acid

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