3 x Jane's age = 8 x Beth's age. Difference between ages is 15 years. How old are Jane and Beth?

Answer 1

3j=8b
j-b=15
j=15+b substitute
3(15+b)=8b
45+3b=8b
5b=45
b=9
j=15+b=15+9=24
3*24=72
8*9=72
beth is 9
jane is 24

Answer 2

Jane: 3x and Beth: 8x and difference means subtraction:

First: 8x - 3x = 15

Second: combine "like" terms:

5x = 15

Third: divide both sides by 5:

5x/5 = 15/5
x = 3

Take (3) and replace it with "x" for Jane's age and Beth's age separately:

Jane = 3(3) = 9
Beth: 3(8) = 24

Answer 3

j = jane's age
b = beth's age

3j = 8b
j-b = 15

solve j-b = 15 for j
j-b=15
j = b+15

substitute j into the other equation
3j = 8b
j = b+15
3(b+15) = 8b

solve for b
3(b+15) = 8b
3b +45 = 8b
-3b -3b
45 = 5b
b = 9

substitute 9 for b in one of the equations
j - b = 15
j - 9 = 15
+9 +9
j = 24

Jane is 24 years old
Beth is 9 years old

Answer 4

Let x be Jane's age and y Beth's age. Then 3x = 8y, and therefore x > y. So x - y = 15. One can now combine these 2 equations:

3x - 8y =0

x - y = 15.

Solving the previous system yields (by substitution for instance)

x = 24 and y= 9.

Answer 5

let Jane,s age be x ,and Beth,s age y
3x=8y then x=8/3y
x-y=15 8/3y-y=15 5/3y=15 (*3/5)
y=9
x=8/3*9=24
Jan,sage 24 Beth,s age 9

Answer 6

let janes age be x
beth's age=3x/8
difference=x-3x/8
=5x/8
given 5x/8=15
multiplying by 8/5
x=15*8/5
=24
jane's age=24 years and beth's age=9 years

Answer 7

jane is 9 and beth is 24

3x = 8x -15
+15 -3x = -3x+15
----------------------
15 = 5x
/5 = /5

x = 3

3*3 = 9, 8*3 = 24, 24 - 9 = 15

Answer 8

3J = 8B
J-B=15

Isolate: J= 15+B
Substitute: 3(15+B)=8B
Solve:
45+3B=8B
5B=45
B=9
and
J=24

Then test:
3J = 8B
3(24) = 8(9)
72 = 72

J-B=15
24-9=15
15=15

Correct

Answer 9

3J=8B
J-B=15

SoBeth is 9 Jane 24

Answer 10

(3J = 8B
(J - B = 15

3J = 8B
J = 8B/3

8B/3 - B = 15
5B = 45
B = 45 : 5
B = 9

J = 8B/3
J = 8.9/3
J = 24
Solution: Jane is 24 y.o and Beth, 9 y.o.
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