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Answer :
Sure! Let's solve this problem step by step.
Larry has some nickels and dimes. We know:
- Larry has 7 more dimes than nickels.
- The total value of his nickels and dimes is $1.45, which is 145 cents.
Let's use the variable [tex]\( n \)[/tex] to represent the number of nickels.
Step 1: Express the number of dimes.
- Since Larry has 7 more dimes than nickels, the number of dimes can be expressed as [tex]\( n + 7 \)[/tex].
Step 2: Calculate the total value of the coins.
- Each nickel is worth 5 cents, so the total value of the nickels is [tex]\( 5n \)[/tex] cents.
- Each dime is worth 10 cents, so the total value of the dimes is [tex]\( 10(n + 7) \)[/tex] cents.
Step 3: Set up the equation.
- According to the problem, the total value of the coins is 145 cents. Therefore, we set up the equation:
[tex]\[
5n + 10(n + 7) = 145
\][/tex]
Step 4: Simplify and solve the equation.
- Distribute the 10 in the equation:
[tex]\[
5n + 10n + 70 = 145
\][/tex]
- Combine the like terms:
[tex]\[
15n + 70 = 145
\][/tex]
- Subtract 70 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
15n = 75
\][/tex]
- Divide both sides by 15 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 5
\][/tex]
Larry has 5 nickels. So, the correct equation from the choices provided is option C: [tex]\( 5n + 10(n + 7) = 145 \)[/tex].
Larry has some nickels and dimes. We know:
- Larry has 7 more dimes than nickels.
- The total value of his nickels and dimes is $1.45, which is 145 cents.
Let's use the variable [tex]\( n \)[/tex] to represent the number of nickels.
Step 1: Express the number of dimes.
- Since Larry has 7 more dimes than nickels, the number of dimes can be expressed as [tex]\( n + 7 \)[/tex].
Step 2: Calculate the total value of the coins.
- Each nickel is worth 5 cents, so the total value of the nickels is [tex]\( 5n \)[/tex] cents.
- Each dime is worth 10 cents, so the total value of the dimes is [tex]\( 10(n + 7) \)[/tex] cents.
Step 3: Set up the equation.
- According to the problem, the total value of the coins is 145 cents. Therefore, we set up the equation:
[tex]\[
5n + 10(n + 7) = 145
\][/tex]
Step 4: Simplify and solve the equation.
- Distribute the 10 in the equation:
[tex]\[
5n + 10n + 70 = 145
\][/tex]
- Combine the like terms:
[tex]\[
15n + 70 = 145
\][/tex]
- Subtract 70 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
15n = 75
\][/tex]
- Divide both sides by 15 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 5
\][/tex]
Larry has 5 nickels. So, the correct equation from the choices provided is option C: [tex]\( 5n + 10(n + 7) = 145 \)[/tex].
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