Please check to see if I did this correctly. This is a 2 part math problem.
1. Janelle has d dimes and n nickles. Her sister has 5 times as many dimes and 6 times as many nickles as Janelle has. Write the sum of the number of coins they have, and then combine like terms.
This is the answer I came to: d+n+5d+6n
2. If Janelle has 9 dimes and 18 nickles, how many total coins do Janelle and her sister have?
This is the answer I came to:
9d x 5d + 18n x 6n = 45 + 108 = 153 coins
it asked to combine like terms, you still have to do that.
= 6d + 7n
Is #2 a continuation of #1 ? I will assume it is
so d = 9 and n = 18
so sum = 6(9) + 7(18) = 180
1. To write the sum of the number of coins Janelle has and the number of coins her sister has, you can simplify the expression: d + n + 5d + 6n.
Combining like terms, you can add up the number of dimes and the number of nickels separately:
d + 5d = 6d
n + 6n = 7n
Now, you can rewrite the expression as: 6d + 7n.
2. If Janelle has 9 dimes and 18 nickels, you can substitute the values into the expression you simplified in step 1:
6d + 7n = 6(9) + 7(18)
Simplifying further:
6(9) = 54
7(18) = 126
Therefore, the total number of coins Janelle and her sister have is 54 + 126 = 180 coins, not 153 as you calculated.
Let's analyze your solutions step by step:
For part 1:
The problem states that Janelle has "d" dimes and "n" nickels.
Her sister has 5 times as many dimes as Janelle, which means her sister has 5d dimes.
Her sister also has 6 times as many nickels as Janelle, which means her sister has 6n nickels.
You correctly wrote the sum of the number of coins they have as: d + n + 5d + 6n.
However, we can simplify this expression by combining like terms.
Combining the dimes (d + 5d) and the nickels (n + 6n) gives us: 6d + 7n.
Therefore, the simplified expression for the number of coins they have is: 6d + 7n.
For part 2:
Given that Janelle has 9 dimes and 18 nickels, we substitute these values into the simplified expression: 6d + 7n.
Replacing d with 9 and n with 18, we get: 6(9) + 7(18) = 54 + 126 = 180.
So, the total number of coins Janelle and her sister have is 180, not 153 as you initially calculated.
In conclusion, for part 2, the correct answer is: Janelle and her sister have a total of 180 coins.