Algebra 1 Worksheets | Word Problems Worksheets - Free Printable

Here's the complete solution to all 10 mixture word problems, with step-by-step explanations.

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Problem 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?

✔ Solution:

Total amount = 11 + 12 = 23 oz

Clay from first soil = 9% of 11 oz = 0.09 × 11 = 0.99 oz
Clay from second soil = 15% of 12 oz = 0.15 × 12 = 1.8 oz

Total clay = 0.99 + 1.8 = 2.79 oz

Clay % in mixture = (2.79 / 23) × 100 ≈ 12.13%

👉 Answer: 12.13%

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Problem 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?

✔ Solution:

Total weight = 7 + 9 = 16 lbs

Red apples from first bag = 36% of 7 = 0.36 × 7 = 2.52 lbs
Red apples from second bag = 32% of 9 = 0.32 × 9 = 2.88 lbs

Total red apples = 2.52 + 2.88 = 5.4 lbs

Percent red = (5.4 / 16) × 100 = 33.75%

👉 Answer: 33.75%

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Problem 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.

✔ Solution:

Total volume = 7 + 13 = 20 L

Vinegar from first = 16% of 7 = 0.16 × 7 = 1.12 L
Vinegar from second = 79% of 13 = 0.79 × 13 = 10.27 L

Total vinegar = 1.12 + 10.27 = 11.39 L

Concentration = (11.39 / 20) × 100 = 56.95%

👉 Answer: 56.95%

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Problem 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?

✔ Solution:

Total weight = 3 + 14 + 4 = 21 lbs

Cost of peanuts = 3 × $3 = $9
Cost of raisins = 14 × $6 = $84
Cost of cashews = 4 × $5 = $20

Total cost = 9 + 84 + 20 = $113

Cost per lb = 113 ÷ 21 ≈ $5.38

👉 Answer: $5.38 per lb

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Problem 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?

✔ Solution:

Let x = percent sugar in cranberry juice (as decimal)

Total volume = 4 + 12 = 16 L

Sugar from apple juice = 44% of 12 = 0.44 × 12 = 5.28 L

Sugar from cranberry juice = x × 4 = 4x L

Total sugar = 5.28 + 4x

Final mixture is 48% sugar → 0.48 × 16 = 7.68 L

Set up equation:

> 5.28 + 4x = 7.68
> 4x = 7.68 - 5.28 = 2.4
> x = 2.4 ÷ 4 = 0.6 → 60%

👉 Answer: 60%

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Problem 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?

✔ Solution:

Let x = mass of coin (in grams)

Gold in coin = 34% of x = 0.34x
Gold in necklace = 100% of 13 = 13 g

Total mass = x + 13
Total gold = 0.34x + 13

Final mixture is 79% gold:

> (0.34x + 13) / (x + 13) = 0.79

Multiply both sides by (x + 13):

> 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 = 2.73 ÷ 0.45 = 6.066... ≈ 6.07 g

👉 Answer: 6.07 grams

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Problem 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.

✔ Solution:

Let x = percent salt in first solution (as decimal)

Salt from first = 12x
Salt from second = 39% of 9 = 0.39 × 9 = 3.51 mL

Total volume = 12 + 9 = 21 mL

Total salt = 12x + 3.51

Final concentration = 56% → 0.56 × 21 = 11.76 mL

Equation:

> 12x + 3.51 = 11.76
> 12x = 11.76 - 3.51 = 8.25
> x = 8.25 ÷ 12 = 0.6875 → 68.75%

👉 Answer: 68.75%

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Problem 8:
Jessica mixed 10 mL of a 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.

✔ Solution:

Let x = percent acid in first solution (as decimal)

Acid from first = 10x
Acid from second = 47% of 3 = 0.47 × 3 = 1.41 mL

Total volume = 10 + 3 = 13 mL

Total acid = 10x + 1.41

Final concentration = 42% → 0.42 × 13 = 5.46 mL

Equation:

> 10x + 1.41 = 5.46
> 10x = 5.46 - 1.41 = 4.05
> x = 4.05 ÷ 10 = 0.405 → 40.5%

👉 Answer: 40.5%

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Problem 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?

✔ Solution:

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

Silver from first = 0.12x
Silver from second = 0.74(5 - x)

Total silver needed = 52% of 5 = 0.52 × 5 = 2.6 lb

Equation:

> 0.12x + 0.74(5 - x) = 2.6
> 0.12x + 3.7 - 0.74x = 2.6
> -0.62x = 2.6 - 3.7 = -1.1
> x = (-1.1) ÷ (-0.62) ≈ 1.774 lb

So, 12% metal = 1.77 lb,
74% metal = 5 - 1.774 ≈ 3.23 lb

👉 Answer: 1.77 lb of 12% silver, 3.23 lb of 74% silver

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

✔ Solution:

Let x = pounds of 63% peanut bag
Then 11 - x = pounds of 25% peanut bag

Peanuts from first = 0.63x
Peanuts from second = 0.25(11 - x)

Total peanuts needed = 56% of 11 = 0.56 × 11 = 6.16 lb

Equation:

> 0.63x + 0.25(11 - x) = 6.16
> 0.63x + 2.75 - 0.25x = 6.16
> 0.38x = 6.16 - 2.75 = 3.41
> x = 3.41 ÷ 0.38 ≈ 8.97 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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✔ All problems solved!
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