Pregunta
Question Lydia has \( n \) nickels and \( d \) dimes. She has no more than Video \( \$ 1 \) worth of coins altogether. Write this situation as an inequality.
Ask by Wyatt Gough. in the United States
Jan 24,2025
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The inequality is \( 0.05n + 0.10d \leq 1 \).
Solución
To express the situation as an inequality, we need to consider the value of the coins Lydia has.
1. **Value of Nickels**: Each nickel is worth \( 0.05 \) dollars. Therefore, the total value of \( n \) nickels is:
\[
0.05n
\]
2. **Value of Dimes**: Each dime is worth \( 0.10 \) dollars. Therefore, the total value of \( d \) dimes is:
\[
0.10d
\]
3. **Total Value**: The total value of the coins Lydia has is the sum of the values of the nickels and dimes:
\[
0.05n + 0.10d
\]
4. **Inequality Condition**: Lydia has no more than \( 1 \) dollar worth of coins. This can be expressed as:
\[
0.05n + 0.10d \leq 1
\]
Thus, the inequality representing the situation is:
\[
0.05n + 0.10d \leq 1
\]
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Simplifique esta solución Beyond the Answer
The total value of Lydia's nickels and dimes must not exceed $1. Since each nickel is worth $0.05 and each dime is worth $0.10, you can express this as an inequality: \[ 0.05n + 0.10d \leq 1 \] This shows that the combined value of Lydia's nickels and dimes is limited to one dollar. To keep things straightforward, you could also multiply the entire inequality by 100 to eliminate the decimals. This gives you \( 5n + 10d \leq 100 \). Both expressions represent the same situation with a slightly different format.
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