Algebra 1 Worksheets | Word Problems Worksheets - Free Printable

Let's solve each of these mixture word problems step by step.

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1) Dan mixed 11 oz of soil containing 9% clay with 12 oz of soil with 15% clay. What is the clay content in the mixture?

- Clay from first soil:
$ 11 \times 0.09 = 0.99 $ oz
- Clay from second soil:
$ 12 \times 0.15 = 1.8 $ oz
- Total clay:
$ 0.99 + 1.8 = 2.79 $ oz
- Total mixture:
$ 11 + 12 = 23 $ oz
- Percent clay:
$ \frac{2.79}{23} \times 100 \approx 12.13\% $

✔ Answer: 12.13%

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2) Keith dumped 7 lbs of a bag of apples with 36% red apples into a bag of 9 lbs which contained 32% red apples. What is the new percent of red apples?

- Red apples from first bag:
$ 7 \times 0.36 = 2.52 $ lbs
- Red apples from second bag:
$ 9 \times 0.32 = 2.88 $ lbs
- Total red apples:
$ 2.52 + 2.88 = 5.4 $ lbs
- Total apples:
$ 7 + 9 = 16 $ lbs
- Percent red:
$ \frac{5.4}{16} \times 100 = 33.75\% $

✔ Answer: 33.75%

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3) A 7 L solution that was 16% vinegar was mixed with a 13 L solution that was 79% vinegar. Find the new concentration of vinegar.

- Vinegar from first:
$ 7 \times 0.16 = 1.12 $ L
- Vinegar from second:
$ 13 \times 0.79 = 10.27 $ L
- Total vinegar:
$ 1.12 + 10.27 = 11.39 $ L
- Total solution:
$ 7 + 13 = 20 $ L
- Concentration:
$ \frac{11.39}{20} \times 100 = 56.95\% $

✔ Answer: 56.95%

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4) Melanie’s trail mix was made combining 3 lbs of peanuts that cost $3/lb, 14 lbs of raisins at $6/lb, and 4 lbs of cashews at $5/lb. What was the cost per lb of the mixture?

- Cost of peanuts:
$ 3 \times 3 = 9 $
- Cost of raisins:
$ 14 \times 6 = 84 $
- Cost of cashews:
$ 4 \times 5 = 20 $
- Total cost:
$ 9 + 84 + 20 = 113 $
- Total weight:
$ 3 + 14 + 4 = 21 $ lbs
- Cost per lb:
$ \frac{113}{21} \approx 5.38 $

✔ Answer: $5.38 per lb

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5) Benny mixed 4 L of cranberry juice into 12 L of apple juice, that had 44% sugar. If the cranapple mixture was 48% sugar, what was the percent of sugar in the cranberry juice?

Let $ x $ be the percent of sugar in cranberry juice (as a decimal).

- Sugar from apple juice:
$ 12 \times 0.44 = 5.28 $ L
- Sugar from cranberry juice:
$ 4x $ L
- Total sugar:
$ 5.28 + 4x $
- Total volume:
$ 4 + 12 = 16 $ L
- Mixture is 48% sugar:
$ \frac{5.28 + 4x}{16} = 0.48 $

Multiply both sides by 16:
$$
5.28 + 4x = 7.68
$$
$$
4x = 2.4
$$
$$
x = 0.6
$$

So, $ x = 60\% $

✔ Answer: 60%

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6) How many g of gold should a coin of 34% gold be if when combined with a 13 g pure gold necklace, it forms a metal that is 79% gold?

Let $ x $ be the mass (in grams) of the 34% gold coin.

- Gold from coin:
$ 0.34x $
- Gold from necklace:
$ 13 $ g (pure)
- Total gold:
$ 0.34x + 13 $
- Total mass:
$ x + 13 $
- Final mixture is 79% gold:

$$
\frac{0.34x + 13}{x + 13} = 0.79
$$

Multiply both sides:
$$
0.34x + 13 = 0.79(x + 13)
$$
$$
0.34x + 13 = 0.79x + 10.27
$$
$$
13 - 10.27 = 0.79x - 0.34x
$$
$$
2.73 = 0.45x
$$
$$
x = \frac{2.73}{0.45} = 6.066... \approx 6.07
$$

✔ Answer: 6.07 g

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7) Alyssa mixed 12 mL of a salt solution with 9 mL of a 39% salt solution to make a 56% salt solution. Find the percent salt concentration of the first solution.

Let $ x $ be the concentration (as decimal) of the first solution.

- Salt from first:
$ 12x $
- Salt from second:
$ 9 \times 0.39 = 3.51 $
- Total salt:
$ 12x + 3.51 $
- Total volume:
$ 12 + 9 = 21 $ mL
- Final concentration:
$ \frac{12x + 3.51}{21} = 0.56 $

Multiply:
$$
12x + 3.51 = 0.56 \times 21 = 11.76
$$
$$
12x = 11.76 - 3.51 = 8.25
$$
$$
x = \frac{8.25}{12} = 0.6875 = 68.75\%
$$

✔ Answer: 68.75%

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8) Jessica mixed 10 mL of an acidic solution with 3 mL of a 47% acidic solution to make a 42% acidic solution. Find the percent acid concentration of the first solution.

Let $ x $ be the concentration of the first solution.

- Acid from first:
$ 10x $
- Acid from second:
$ 3 \times 0.47 = 1.41 $
- Total acid:
$ 10x + 1.41 $
- Total volume:
$ 10 + 3 = 13 $ mL
- Final concentration:
$ \frac{10x + 1.41}{13} = 0.42 $

Multiply:
$$
10x + 1.41 = 0.42 \times 13 = 5.46
$$
$$
10x = 5.46 - 1.41 = 4.05
$$
$$
x = 0.405 = 40.5\%
$$

✔ Answer: 40.5%

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9) Sam needs 5 lb of metal with 52% silver. If Sam combines one metal with 12% silver, and another with 74% silver, how much of each metal does Sam need?

Let $ x $ = amount of 12% silver metal
Then $ 5 - x $ = amount of 74% silver metal

Total silver:
$$
0.12x + 0.74(5 - x) = 0.52 \times 5 = 2.6
$$

Solve:
$$
0.12x + 3.7 - 0.74x = 2.6
$$
$$
-0.62x = 2.6 - 3.7 = -1.1
$$
$$
x = \frac{-1.1}{-0.62} \approx 1.774 \text{ lb}
$$

So:
- 12% silver: 1.774 lb
- 74% silver: $ 5 - 1.774 = 3.226 $ lb

✔ Answer:
1.77 lb of 12% silver, 3.23 lb of 74% silver (rounded to nearest hundredth)

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10) Tim has two bags of nuts: one with 63% peanuts, and the other with 25% peanuts. To make an 11 lb bag of 56% peanuts, how much of each should Tim use?

Let $ x $ = amount from 63% bag
Then $ 11 - x $ = amount from 25% bag

Peanuts:
$$
0.63x + 0.25(11 - x) = 0.56 \times 11 = 6.16
$$

Solve:
$$
0.63x + 2.75 - 0.25x = 6.16
$$
$$
0.38x = 6.16 - 2.75 = 3.41
$$
$$
x = \frac{3.41}{0.38} \approx 8.974 \text{ lb}
$$

So:
- 63% bag: 8.97 lb
- 25% bag: $ 11 - 8.97 = 2.03 $ lb

✔ Answer:
8.97 lb of 63% peanuts, 2.03 lb of 25% peanuts

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 12.13% |
| 2 | 33.75% |
| 3 | 56.95% |
| 4 | $5.38 per lb |
| 5 | 60% |
| 6 | 6.07 g |
| 7 | 68.75% |
| 8 | 40.5% |
| 9 | 1.77 lb (12%), 3.23 lb (74%) |
| 10 | 8.97 lb (63%), 2.03 lb (25%) |

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