Here is the step-by-step solution to
Problem 1 from your worksheet:
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Problem 1:
> A collection of 105 coins consists of 1.00 peso and 5.00 pesos. If the total value is 205.00 pesos, find the number of coins of each denomination in the collection.
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##
✔ Step 1: Define Variables
Let:
- \( x \) = number of
1.00 peso coins
- \( y \) = number of
5.00 peso coins
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##
✔ Step 2: Write Equations Based on Given Information
We are told two things:
1.
Total number of coins is 105
→ \( x + y = 105 \)
2.
Total value is 205.00 pesos
→ \( 1x + 5y = 205 \)
(since each 1-peso coin contributes 1 peso, and each 5-peso coin contributes 5 pesos)
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##
✔ Step 3: Solve the System of Equations
We have:
\[
\begin{cases}
x + y = 105 \quad \text{(Equation 1)} \\
x + 5y = 205 \quad \text{(Equation 2)}
\end{cases}
\]
Subtract Equation 1 from Equation 2 to eliminate \( x \):
\[
(x + 5y) - (x + y) = 205 - 105
\]
\[
x + 5y - x - y = 100
\]
\[
4y = 100
\]
\[
y = 25
\]
Substitute \( y = 25 \) into Equation 1:
\[
x + 25 = 105
\]
\[
x = 105 - 25 = 80
\]
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##
✔ Final Answer:
-
Number of 1.00 peso coins: 80
-
Number of 5.00 peso coins: 25
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##
✔ Verification:
- Total coins: \( 80 + 25 = 105 \)
✔
- Total value: \( 80 \times 1 + 25 \times 5 = 80 + 125 = 205 \) pesos
✔
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✔ The solution satisfies both conditions.
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If you'd like me to solve any other problem from this list (e.g., Problem 2, 3, etc.), just let me know which one! I can walk through each one with full explanation.
Parent Tip: Review the logic above to help your child master the concept of two variable word problems worksheet.
