3x3 Systems of Equations Word Problems Activity for Google Slides ™ - Free Printable

Let’s solve this step by step.

We are told:
- Malika has $17.00 in quarters, dimes, and nickels.
- She has 10 more dimes than quarters.
- She has 130 coins total.
- We need to find how many of each coin she has.

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Step 1: Declare your variables

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

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Step 2: Write the system of equations

Equation 1 (total value):
Each quarter is $0.25, dime is $0.10, nickel is $0.05. Total is $17.00.
→ 0.25q + 0.10d + 0.05n = 17.00

Equation 2 (dimes vs quarters):
She has 10 more dimes than quarters.
→ d = q + 10

Equation 3 (total coins):
Total coins = 130
→ q + d + n = 130

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Step 3: Solve the system

We can substitute Equation 2 into Equations 1 and 3 to eliminate d.

First, plug d = q + 10 into Equation 3:

q + (q + 10) + n = 130
→ 2q + 10 + n = 130
→ 2q + n = 120
→ n = 120 - 2q ← Let’s call this Equation A

Now plug d = q + 10 and n = 120 - 2q into Equation 1:

0.25q + 0.10(q + 10) + 0.05(120 - 2q) = 17.00

Let’s compute each term:

0.25q
+ 0.10q + 1.00 ← because 0.10 × 10 = 1.00
+ 0.05×120 = 6.00, and 0.05×(-2q) = -0.10q → so +6.00 - 0.10q

Now combine all:

0.25q + 0.10q + 1.00 + 6.00 - 0.10q = 17.00

Combine like terms:

(0.25q + 0.10q - 0.10q) + (1.00 + 6.00) = 17.00
→ 0.25q + 7.00 = 17.00

Subtract 7.00 from both sides:

0.25q = 10.00

Divide both sides by 0.25:

q = 10.00 / 0.25 = 40

So, quarters = 40

Now find dimes:
d = q + 10 = 40 + 10 = 50

Now find nickels:
n = 120 - 2q = 120 - 80 = 40

Check total coins: 40 + 50 + 40 = 130 ✔

Check total value:
Quarters: 40 × 0.25 = $10.00
Dimes: 50 × 0.10 = $5.00
Nickels: 40 × 0.05 = $2.00
Total: $10 + $5 + $2 = $17.00 ✔

Everything checks out!

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Final Answer:
Malika has 40 quarters, 50 dimes, and 40 nickels.