Answer:
Part a) 2.36 quarts
Part b) 47.2%
Step-by-step explanation:
Let
x ---> percentage of the resulting mixture that is antifreeze
Remember that
[tex]22\%=22/100=0.22[/tex]
[tex]85\%=85/100=0.85[/tex]
we know that
3 quarts of a solution multiplied by 0.22 (percentage in decimal form) plus 2 quarts of a solution multiplied by 0.85 (percentage in decimal form), must be equal to 5 quarts of a solution multiplied by x (percentage of the resulting mixture)
so
The linear equation that represent this situation is
[tex]3(0.22)+2(0.85)=(3+2)x[/tex]
solve for x
[tex]0.66+1.7=5x\\5x=2.36\\x=0.472[/tex]
Convert to percentage
[tex]0.472*100=47.2\%[/tex]
therefore
The percentage of the resulting mixture that is antifreeze is 47.2%
To find out how many quarts of antifreeze are in the resulting mixture, multiply the total quarts of the resulting mixture by the percentage in decimal form
[tex]5(0.472)=2.36\ quarts[/tex]
The number of quarts of antifreeze in the resulting mixture is 0.472
let
The equation
3(22%) + 2(85%) = x(3+2)
3(0.22) + 2(0.85) = x(5)
0.66 + 1.7 = 5x
2.36 = 5x
x = 2.36/5
= 0.472
Percentage of the resulting mixture is antifreeze = 0.472 × 100
= 47.2%
The percentage of the resulting mixture is antifreeze is 47.2%
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