I need help for math problems!?

Question

Use a system of equations and substitution to solve each problem:

1) How much of a 10% saline solution should be mixed with a 20% saline solution to obtain 1000 milliliters of a 12% saline solution?

2)The ten digits of a two digits number is 3 greater than the units digit.

Eight times the sum of the digits is 1 less than the number. Find the number.

Thank you very much

Kisses from Spain

Answer 1

Let x be the amount of 10% solution and y be the amount of 20% solution

You want to end up with 1000 mL, so x+y=1000

Solve for y, y=1000 - x

For the second equation, you multiply % by amount for every piece:

10x+20y=12*1000

Substitute in the known y

10x+20(1000-x)=12000

10x+20000-20x=12000

-10x+20000=12000

-10x=-8000

x=800

y=200

800 mL of 10% solution

200 mL of 20% solution

Let x be the digit in the 10s position and y be the digit in the 1s position.  Then the number is 10x+y

x=3+y

8*(x+y)=(10x+y)-1

8x+8y=10x+y-1

-2x+7y=-1

Substitute in for x:

-2*(3+y)+7y=-1

-6+-2y+7y=-1

-6+5y=-1

5y=5

y=1

Since x=3+y, x=3+1=4

The number is 41

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