Question

Write a systems of equations for each problem define variables used. Please show all work.On a table are 20 coin., quarters and dimes. Their value is $3.05 how many of each kind of coin are there?

Answer 1

We have 20 coins in total, lets say that we have X amount od quarters(0.25 dollar) and Y amount of dimes(0.1 dollar), and in total we have $3.05, with this we can write the system:

`X+Y=20`

Wich means that we have 20 coins, and:

`0.25X\text{ + 0.1Y=3.05}`

Thats the amount of money we have.

So, from the first equation, we can isolate X, as follows:

`X=20-Y`

And with that we can substitute X in the second equation, as follows:

`0.25X\text{ + 0.1Y=3.05 }\rightarrow\text{ }0.25(20-Y)\text{ + 0.1Y=3.05 }\rightarrow\text{ }5-0.25Y+0.1Y=3.05`
`5-0.25Y+0.1Y=3.05\rightarrow-0.15Y=-1.95\rightarrow Y=13`

So, if Y=13, we have that X=7. So 13 dimes and 7 quarters.