SOLUTION: the sum of the ages of two sister's is 37.the difference between four times the older sister's and three times the younger sister's age is 43.find the age of each sister.

Question 165127: the sum of the ages of two sister's is 37.the difference between four times the older sister's and three times the younger sister's age is 43.find the age of each sister.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Let x = younger sister's age
and y = older sister's age
.
Since we have two unknowns, we'll need two equations.
.
Equation 1: "the sum of the ages of two sister's is 37"
x+y = 37
.
Equation 2: "the difference between four times the older sister's and three times the younger sister's age is 43"
4y - 3x = 43
.
Using the substitution method, solve equation 1 for y:
x+y = 37
y = 37-x
.
Substitute the above into equation 2 and solve for x:
4y - 3x = 43
4(37-x) - 3x = 43
148 - 4x - 3x = 43
148 - 7x = 43
148 = 7x+43
105 = 7x
15 years = x (younger sister's age)
.
Older sister's age, if found by plugging the above into equation 1 and solving for y:
x+y = 37
15+y = 37
y = 22 years (older sister's age)

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