How many gallons of a $$ 60 \% $$ antifreeze solution must be mixed with 70 gallons of $$ 20 \% $$ antifreeze to get a mixture that is $$ 50 \% $$ antifreeze? Use the six-step method. You need $$ \square $$ gallons. (Round to the nearest whole number.) 1

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1. Let $$ x $$ be the number of gallons of $$ 60\% $$ antifreeze solution to be mixed.

2. The amount of pure antifreeze in the $$ x $$ gallons is $$ 0.6x $$ and in the 70 gallons of $$ 20\% $$ solution is $$ 0.2 \times 70 $$.

3. The total amount of pure antifreeze in the mixture is:
   $$
   0.6x + 0.2 \times 70
   $$

4. The total volume of the mixture is $$ x + 70 $$. The desired concentration is $$ 50\% $$, hence the mixture should contain:
   $$
   0.5(x + 70)
   $$

5. Set up the equation based on the pure antifreeze amounts:
   $$
   0.6x + 0.2 \times 70 = 0.5(x + 70)
   $$
   Simplify:
   $$
   0.6x + 14 = 0.5x + 35
   $$

6. Solve the equation:
   $$
   0.6x - 0.5x = 35 - 14
   $$
   $$
   0.1x = 21
   $$
   $$
   x = \frac{21}{0.1} = 210
   $$

You need $$ 210 $$ gallons of the $$ 60\% $$ antifreeze solution.
You need 210 gallons of the 60% antifreeze solution.

How many gallons of a antifreeze solution must be mixed with 70 gallons of antifreeze to get a mixture that is antifreeze? Use the six-step method.
You need gallons.
(Round to the nearest whole number.) 1

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How many gallons of a antifreeze solution must be mixed with 70 gallons of antifreeze to get a mixture that is antifreeze? Use the six-step method. You need gallons. (Round to the nearest whole number.) 1