Worksheet with five word problems requiring the setup and solution of systems of equations.

Let’s solve each problem one by one, step by step. We’ll define variables, set up equations, and solve them carefully.

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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 that 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 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 ✔️

So, squash costs $0.18, zucchini costs $0.21.

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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 to make the b terms match:

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 j = 5 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 ✔️

Judy earns $5/hour, Ben earns $4/hour.

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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 ✔️
Coins: 16 + 24 = 40 ✔️

Rob has 16 dimes and 24 quarters.

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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

Kelly has 8 quarters.

✔ Check:
If q=8, then d=16
Value: 16×0.10 = 1.60, 8×0.25 = 2.00 → total $3.60 ✔️

Answer: 8 quarters.

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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 × $3 = $1140
150 × $4 = $600
Total = $1740 ✔️
Tickets: 380 + 150 = 530 ✔️

Student tickets: 380, Adult tickets: 150.

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Final Answer:
1. Squash: $0.18, Zucchini: $0.21
2. Judy: $5/hour, Ben: $4/hour
3. 16 dimes, 24 quarters
4. 8 quarters
5. 380 student tickets, 150 adult tickets