Answer:
1 quart must be added
Step-by-step explanation:
To do this, set up an equation.
Let x be the number of quarts of antifreeze to be added. Then, you know that the new solution will have a total of 4 quarts with 2/5 of it being antifreeze, so [tex]\frac{2}{5} (x+3)[/tex] would be the amount of antifreeze. Another way to represent the amount of antifreeze is [tex]x + \frac{3}{5}[/tex] because the original mixture has 3/5 of quart of antifreeze, while the added stuff is fully antifreeze.
Now, you just solve the equation:
[tex]\frac{2}{5} (x + 3) = x + \frac{3}{5}[/tex]
multiply both sides by 5
[tex]2(x + 3) = 5x + 3[/tex]
Use the distributive property on the left
[tex]2x + 6 = 5x + 3[/tex]
subtract 2x from both sides
[tex]6 = 3x + 3[/tex]
subtract 3 from both sides
[tex]3 = 3x[/tex]
divide both sides by 3
[tex]1 = x \\x = 1[/tex]
Therefore the answer is 1 quart
