SOLUTION: thirteen years ago, Mary's age was 5/17 of Grace's age. Two years from now Mary will be 1/2 of Jim's age. Together all their ages add up to 118. Find their ages five years from now
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-> SOLUTION: thirteen years ago, Mary's age was 5/17 of Grace's age. Two years from now Mary will be 1/2 of Jim's age. Together all their ages add up to 118. Find their ages five years from now
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Question 159384This question is from textbook Prentice Hall Algebra 1
: thirteen years ago, Mary's age was 5/17 of Grace's age. Two years from now Mary will be 1/2 of Jim's age. Together all their ages add up to 118. Find their ages five years from now. This question is from textbook Prentice Hall Algebra 1
You can put this solution on YOUR website! We know that 13 years ago Mary was 5/17 Grace's age. This is algebraically
written as M-13=5/17G
M=Mary's age now
G=Grace's age now
J=Jim's age now
Two years from now Mary will be 1/2 of Jim's age. We write this algebraically as:
1/2J=(M+2)
We also know that J+M+G=118
Isolate J by mutilplying both sides by to get
J=2(M+2)
Isolate G by Multiplying both sides of the equation by 17/5 to get
17/5(M-13)=G
Substitute J=2(M+2)
and G=17/5(M-13)
into 2(M+2) +17/5(M-13) +M=118
Multiply all the terms by 5 to get rid of the denominator
10(M+2)+17(M-13)+5M=590
Use the distributive property
10M+20+17M-221+5M=590
Combine like terms and simplify the equation.
(10+17+5)M-201=590
32M-201=590
Add 201 to both sides of the equation
32M=791
Divide by 32 on both sides
and get 24.7 Round up and it would be 25
Plug in to see if it makes sense.
1/2J=(M+2)
Mary would be 27 and Jim would be 54
25+54+G=118
Grace would be 39
(25-13)=5/17(39)
12=11.5 Round up would be 12.
Therefore in 5 years Mary=30 Grace=44 Jim=59
You can put this solution on YOUR website! thirteen years ago, Mary's age was 5/17 of Grace's age. Two years from now Mary will be 1/2 of Jim's age. Together all their ages add up to 118. Find their ages five years from now.
:
Let m = Mary's age now
Let g = Grace's age now
:
Write an equation/expression for each statement
:
"thirteen years ago": that would be:
(m-13) and (g-13)
:
" Mary's age was 5/17 of Grace's age."
m - 13 = (g-13)
Multiply equation by 17 to get rid of that annoying denominator, results:
17(m-13) = 5(g-13)
17m - 221 = 5g - 65
or
5g - 65 = 17m - 221
5g = 17m - 221 + 65
5g = 17m - 156
g =
;
" Two years from now Mary will be 1/2 of Jim's age."
Where did Jim come from? Anyway: j = jim's age now:
:
(m+2) = .5(j+2)
or
j + 2 = 2(m+2)
j = (2m+4) - 2
j = 2m + 2
:
Together all their ages add up to 118.
m + g + j = 118
:
Substitute for g and j
m + + (2m+2) = 118
Multiply equation by 5, results:
5m + (17m-156) + 5(2m+2) = 5(118)
5m + 17m - 156 + 10m + 10 = 590
32m - 146 = 590
32m = 590 + 146
32m = 736
m =
m = 23 yrs is Mary's present age
then
j = 2(23)+ 2)
j = 46 + 2
j = 48 yrs is Jim's present age
and
g =
g =
g =
g = 47 yrs is Grace's present age
:
Check 23 + 48 + 47 = 118
:
Find their ages five years from now. Just add 5 to the above ages:
Mary 28, Grace 52, Jim 53
