SOLUTION: translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.

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Question 297822: translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
A sum of money amounting to $3.80 consists of dimes and quarters. If there are 20 coins in all, how many are quarters?
Answer by blwinbbbles(106) (Show Source):
You can put this solution on YOUR website!
so let's first make the equations x=dimes y=quarters
There are x number of dimes and y number of quarters and together the make up 20 coins.
so x+y=20 and if dimes are .10 and quarters are .25 then you can say
.10x + .25y = 3.80
Now you have the two equations
1) x + y = 20
2) .10x + .25y = 3.80
Let's use substitution and use equation 1, which we can rearrange to say
x = 20-y now sub that into x in equation 2
.10(20-y)+ .25y = 3.80
2.0 - .10y +.25y = 3.80
2.0 + .15y = 3.80 subtract 2.0 from both sides
.15y = 1.80 divide by .15
y = 12
so there are 12 quarters...use y = y back into equation 1
x + 12 = 20 subtract 12 from both sides
x = 8
so there are 8 dimes and 12 quarters