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Idil has some dimes and some quarters. She has no less than coins worth no more than combined. If Idil has dimes, determine the maximum number of quarters that she could have.Answer:
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Q. Idil has some dimes and some quarters. She has no less than coins worth no more than combined. If Idil has dimes, determine the maximum number of quarters that she could have.Answer:
- Calculate total value of dimes: First, let's calculate the total value of the dimes that Idil has.Since each dime is worth , the value of dimes is $\(8\) \times \$\(0\).\(10\).
- Calculate value of dimes: Now, let's calculate the value of the \(8\) dimes.\(8\) dimes \(*\) \(\$0.10/\)dime = \(\$0.80\).
- Determine remaining amount for quarters: Next, we need to determine the remaining amount of money that could be in quarters. Since the total value cannot exceed \(\$3.60\), we subtract the value of the dimes from \(\$3.60\). \(\$3.60 - \$0.80 = \$2.80\). This is the maximum amount that could be in quarters.
- Find maximum number of quarters: Now, let's find out the maximum number of quarters that could make up this amount.\(\newline\)Since each quarter is worth \(\$0.25\), we divide \(\$2.80\) by \(\$0.25\).
- Calculate number of quarters: Calculating the number of quarters gives us:\(\newline\)\(\$2.80 / \$0.25/\text{quarter} = 11.2\) quarters.\(\newline\)However, since we cannot have a fraction of a quarter, we need to round down to the nearest whole number.
- Determine maximum quarters: The maximum whole number of quarters Idil could have is \(11\) quarters.
- Check total number of coins: Finally, we need to check if having \(11\) quarters along with \(8\) dimes gives us at least \(18\) coins in total.\(\newline\)\(8\) dimes \(+\) \(11\) quarters \(=\) \(19\) coins.\(\newline\)This satisfies the condition of having no less than \(18\) coins.
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