Answers:
- <u>20 pounds</u> of the 95% concrete mix
- <u>10 pounds</u> of the 80% concrete mix
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Explanation:
x = amount of the 95% concrete mix
y = amount of the 80% concrete mix
Type A mix has 95% concrete. If we have x pounds of this, then 0.95x pounds is pure concrete. Type B mix has 80% concrete. If there are y pounds of this, then 0.80y pounds is pure concrete.
So far we have 0.95x+0.80y pounds of pure concrete from the two mixes
Divide this over 30 to get (0.95x+0.80y)/30
Setting this equal to 0.90 means we want the final mix to be 90% concrete.
Since we want 30 pounds total, we can say x+y = 30 which solves to y = 30-x. We'll use this later
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(0.95x+0.80y)/30 = 0.90
0.95x+0.80y = 30*0.90 .... multiply both sides by 30
0.95x+0.80y = 27
0.95x+0.80(30-x) = 27 ..... plug in y = 30-x
0.95x+0.80*30-0.80*x = 27
0.95x+24-0.80x = 27
0.15x+24 = 27
0.15x = 27-24 ..... subtracting 24 from both sides
0.15x = 3
x = 3/0.15 ........... dividing both sides by 0.15
x = 20
y = 30-x
y = 30-20
y = 10
