Question

Jackson has a coin collection consisting of quarters and dimes. The total value of hiscollection is $20.45. His collection consists of ten less quarters than three times thenumber of dimes. Using the variables q and d to represent the number of quarters inhis collection and the number of dimes in his collection respectively, determine asystem of equations that describes the situation.Enter the equations below separated by a comma.How many dimes are in his collection?How many quarters are in his collection?Pls see the picture

Answer 1

Given that,

the variables q and d to represent the number of quarters in his collection and the number of dimes in his collection respectively.

The total value of his collection is $20.45. His collection consists of ten less quarters than three times the number of dimes.

we get,

q=3d-10

Also,

`0.25q+0.1d=20.45`

Substitute q=3d-10 we get

`0.25(3d-10)+0.1d=20.45`
`0.75d-2.5+0.1d=20.45`
`0.85d-2.5=20.45`

`\begin{gathered} 0.85d=22.95 \\ d=(22.95)/(0.85) \end{gathered}`
`d=27`

Substitute d in q=3d-10,

we get,

`q=3(27)-10`
`\begin{gathered} q=81-10=71 \\ q=71 \end{gathered}`

Enter the equations below separated by a comma.

q=3d-10 , 0.25q+0.10d=20.45

How many dimes are in his collection? The number of dimes is 27

How many quarters are in his collection? The number of quarters is 71