Solving Word Problems Using Systems Of Equations Worksheet - Free Printable

Let’s solve each problem one by one. We’ll use systems of equations — that means we’ll write two equations based on the information, then solve them together to find the unknowns.

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Problem 1: Squash and Zucchini

Let:
- s = cost of one squash (in dollars)
- z = cost of one zucchini (in dollars)

From the problem:

Equation 1: 5s + 2z = 1.32
Equation 2: 3s + z = 0.75

We can solve Equation 2 for z:

z = 0.75 - 3s

Now plug this into Equation 1:

5s + 2(0.75 - 3s) = 1.32
5s + 1.50 - 6s = 1.32
-s + 1.50 = 1.32
-s = 1.32 - 1.50
-s = -0.18
→ s = 0.18

Now plug back to find z:

z = 0.75 - 3(0.18) = 0.75 - 0.54 = 0.21

✔ Check:
5(0.18) + 2(0.21) = 0.90 + 0.42 = 1.32 ✔️
3(0.18) + 0.21 = 0.54 + 0.21 = 0.75 ✔️

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Problem 2: Judy and Ben’s Pay

Let:
- j = Judy’s hourly rate
- b = Ben’s hourly rate

Equation 1: 8j + 10b = 80
Equation 2: 9j + 5b = 65

Let’s eliminate one variable. Multiply Equation 2 by 2:

2*(9j + 5b) = 2*65 → 18j + 10b = 130

Now subtract Equation 1 from this:

(18j + 10b) - (8j + 10b) = 130 - 80
10j = 50 → j = 5

Plug into Equation 2:

9(5) + 5b = 65 → 45 + 5b = 65 → 5b = 20 → b = 4

✔ Check:
8(5) + 10(4) = 40 + 40 = 80 ✔️
9(5) + 5(4) = 45 + 20 = 65 ✔️

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Problem 3: Rob’s Coins (Dimes and Quarters)

Let:
- d = number of dimes
- q = number of quarters

Total coins: d + q = 40
Total value: 0.10d + 0.25q = 7.60

Solve first equation for d: d = 40 - q

Plug into second equation:

0.10(40 - q) + 0.25q = 7.60
4 - 0.10q + 0.25q = 7.60
4 + 0.15q = 7.60
0.15q = 3.60
q = 3.60 / 0.15 = 24

Then d = 40 - 24 = 16

✔ Check:
16 dimes = $1.60, 24 quarters = $6.00 → total $7.60 ✔️
16 + 24 = 40 coins ✔️

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Problem 4: Kelly’s Dimes and Quarters

Let:
- d = number of dimes
- q = number of quarters

Total coins: d + q = 24
Total value: 0.10d + 0.25q = 3.60

Solve first equation for d: d = 24 - q

Plug into second:

0.10(24 - q) + 0.25q = 3.60
2.40 - 0.10q + 0.25q = 3.60
2.40 + 0.15q = 3.60
0.15q = 1.20
q = 1.20 / 0.15 = 8

So Kelly has 8 quarters.

✔ Check:
If q=8, then d=16
Value: 16*0.10 + 8*0.25 = 1.60 + 2.00 = 3.60 ✔️

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Problem 5: Talent Show Tickets

Let:
- s = number of student tickets
- a = number of adult tickets

Total tickets: s + a = 530
Total money: 3s + 4a = 1740

Solve first equation for s: s = 530 - a

Plug into second:

3(530 - a) + 4a = 1740
1590 - 3a + 4a = 1740
1590 + a = 1740
a = 1740 - 1590 = 150

Then s = 530 - 150 = 380

✔ Check:
380 student tickets × $3 = $1140
150 adult tickets × $4 = $600
Total = $1740 ✔️
Total tickets = 380 + 150 = 530 ✔️

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Final Answer:

1. Squash: $0.18, Zucchini: $0.21
2. Judy: $5/hour, Ben: $4/hour
3. Rob has 16 dimes and 24 quarters
4. Kelly has 8 quarters
5. 380 student tickets and 150 adult tickets were sold