Question

Mary collected $2.75 in nickels and dimes. Ten less than twice the number of nickels represents the number of dimes she has. How many of each kind of coin does she have?

Answer 1

Mary has 15 nickels and 20 dimes.

Step-by-step explanation:

Let's solve this problem step-by-step:

1. Let's assume the number of nickels as N and the number of dimes as D.
2. According to the given information, the value of the nickels is 0.05N and the value of the dimes is 0.10D.
3. The total amount collected is $2.75, so we can write the equation:

• 0.05N + 0.10D = 2.75

According to the second piece of information, ten less than twice the number of nickels represents the number of dimes. So, we can write another equation:

• D = 2N - 10

We now have a system of two equations with two variables:

• 0.05N + 0.10D = 2.75
• D = 2N - 10

Solve the system of equations to find the values of N and D.Substitute the value of D from the second equation into the first equation:

• 0.05N + 0.10(2N - 10) = 2.75

Expand and simplify the equation:

• 0.05N + 0.20N - 1 = 2.75
• 0.25N - 1 = 2.75
• 0.25N = 3.75
• N = 3.75/0.25
• N = 15

Substitute the value of N into the second equation to find the value of D:

• D = 2(15) - 10
• D = 30 - 10
• D = 20

Therefore, Mary has 15 nickels and 20 dimes.:

Answer 2

Answer: There are 15 nickles and 20 dimes.

Step-by-step explanation:

Since we have given that

Let the number of nickles be 'x'

Let the number of dimes be '2x-10'.

Total amount = $2.75

According to question, we get that

`0.1(2x-10)+0.05x=2.75\\\\0.2x-1+0.05x=2.75\\\\0.25x=2.75+1\\\\0.25x=3.75\\\\x=(3.75)/(0.25)\\\\x=15`

Hence, there are 15 nickles and
`2x-10=2(15)-10=30-10=20` dimes.

Therefore, there are 15 nickles and 20 dimes.