QuestionTheresa has \nq0.05n + 0.25q = 12$.
Studdy Solution
STEP 1
Assumptions1. Theresa has 0.05.
3. The value of a quarter is 12.
STEP 2
Let's denote the number of nickels as and the number of quarters as . We can set up two equations based on the information given in the problem.
1. The total value of all coins is $However, we don't have a value for the total number of coins yet, so we can't use this equation.
STEP 3
To make the calculations easier, we can multiply the first equation by20 to get rid of the decimals. This gives us
STEP 4
Now we need to solve this equation for either or . Let's solve it for
STEP 5
Now we need to find values of (quarters) that will give us a positive integer value for (nickels), since we can't have a fraction of a coin.
STEP 6
If we start with , we find that , which is not a reasonable number of nickels (it would be more than q$.
STEP 7
If we try , we get , which is still too high. We continue this process until we find a reasonable value for .
STEP 8
When we try , we get . This means that Theresa has48 quarters and no nickels, which adds up to $12.
So, Theresa has48 quarters and no nickels.
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