Lesson Using 1 variable as well as using 2 variables(substitution method)

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If a person has three times as many quarters as dimes and the total amount of money is 5.95, find the number of quarters and dimes.

*******************Using 1 variable:************************

Let the number of dimes = x
The value of dimes=10x
The number of quarters= 3x
The value of quarters= 3(25x)
The total amt of money= 5.95
Convert to cents=5.95*100=595 cents
(1 Dollar=100 cents)

10x%2B3%2825x%29=595
85x=595
x=7

The number of dimes=7
The number of quarters= 7*3=21


************************Using Substitution Method:*******************

Let the number of dimes=d
The number of quarters=q
We know that the quarters are 3 times the dimes
So q=3d

The value of quarters=25q
The value of dimes= 10d
The total amount of money is 5.95
Convert it to cents =5.95*100=595
(1 Dollar = 100cents)
25q%2B10d=595
substitute q with 3d in the above equation ***(as we know that q=3d)***
25%283d%29%2B10d=595
75d%2B10d=595
85d=595
d=7
So number of dimes=7.
number of Quarters=3*7=21.









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