Let <em>q</em> be the number of quarts of pure antifreeze that needs to be added to get the desired solution.
8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.
The new solution would have a total volume of 8 + <em>q</em> quarts, and it would contain a total amount of 3.2 + <em>q</em> quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means
(3.2 + <em>q</em>) / (8 + <em>q</em>) = 0.60
Solve for <em>q</em> :
3.2 + <em>q</em> = 0.60 (8 + <em>q</em>)
3.2 + <em>q</em> = 4.8 + 0.6<em>q</em>
0.4<em>q</em> = 1.6
<em>q</em> = 4
Spilt into two figures
first one = 10 x 8 x 14 = 1120
second one = 10 x 10 x 8 = 800
Total volume = 1120 + 800 = 1920 cubic cm
Let n represent the amount Colin earned on Sunday.
On Sat. he earned n/2; on Sun. he earned n; and on Friday he earned (1/2)(n/2).
Then n/2 + n + n/4 = $70
Mult. all terms by 4 to eliminate fractions:
2n + 4n + n = $280
7n = $280 => n = $40
Colin earned n/2, or $20, on Saturday; n, or $40, on Sunday; and n/4, or $10, on Friday.
Note that $20 and $40 and $10 add up to $70, as they must.
