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Question 147349: Kelly is two years yonger than Kristen. If twice Kristen's age is increased by five times Kelly's age the sum is 53. Find the ages of the two girls. I came up wiht Kristen 8.14 and Kelly 6.14.......that is two years less, but it doesn't work.: Kelly is two years yonger than Kristen. If twice Kristen's age is increased by five times Kelly's age the sum is 53. Find the ages of the two girls. I came up wiht Kristen 8.14 and Kelly 6.14.......that is two years less, but it doesn't work.
Answer by ankor@dixie-net.com(3946) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement
Kelly is two years younger than Kristen.
Ke = Kr - 2
:
If twice Kristen's age is increased by five times Kelly's age the sum is 53.
2Kr + 5Ke = 53
:
Find the ages of the two girls.
:
from the 1st equation; substitute(Kr-2) for Ke in the above equation:
2Kr + 5(Kr-2) = 53
:
2Kr + 5Kr - 10 = 53
:
Kr = 53 + 10
Kr = 63/7
Kr = 9 yrs old
then
Ke = 9 - 2 = 7 yrs old
:
:
Check solution in the statement:
"twice Kristen's age is increased by five times Kelly's age the sum is 53."
2(9) + 5(7) =
18 + 35 = 53
Question 147349: Kelly is two years yonger than Kristen. If twice Kristen's age is increased by five times Kelly's age the sum is 53. Find the ages of the two girls. I came up wiht Kristen 8.14 and Kelly 6.14.......that is two years less, but it doesn't work.: Kelly is two years yonger than Kristen. If twice Kristen's age is increased by five times Kelly's age the sum is 53. Find the ages of the two girls. I came up wiht Kristen 8.14 and Kelly 6.14.......that is two years less, but it doesn't work.
Answer by ptaylor(1184) About Me  (Show Source):
You can put this solution on YOUR website!

Let x=Kristen's age; 2x =twice Kristen's age
Then x-2=Kelly's age; 5(x-2)=5 times Kelly's age
2x+5(x-2)=twice Kristen's age increased by 5 times Kelly's age and we are told this equals 53. So our equation to solve:
2x+5(x-2)=53 get rid of parens (distributive law)
2x+5x-10=53 add 10 to each side
2x+5x-10+10=53+10 collect like terms
7x=63 divide each side by 7
x=9----------------------Kristen's age
x-2=9-2=7--------------Kelly's age
CK
2*9+5*7=53
18+35=53
53=53
Hope this helps---ptaylor