Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

I need help again u guys with another Algebra 1 prob. Thnx 4 ur help.?

Here is the problem (showing the work would help me to understand the problem more):

Six years ago, Joe Foster was two years more than five times as old as his daughter. Six years from now, he will be 11 years more than twice as old as she will be. How old is Joe?

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  • Drew
    Lv 5
    1 decade ago
    Favorite Answer

    Let x = Joe's daughter's age six years ago

    So six years ago, Joe was (5x + 2) years old.

    Joe's daughter is now (x + 6) yrs old and Joe is (5x + 2 + 6) yrs old, or 5x + 8..

    In 6 yrs from now, Joe will be 5x + 8 + 6 yrs old, or 5x + 14.

    His daughter will be x + 6 + 6 yrs old or x + 12 yrs old.

    Also, he will be 2(x + 12) + 11 yrs old.

    We now have two expressions that are equal. Joe will be 5x + 14 in six years. He will also be 2(x + 12) + 11 yrs old at that time.

    So, 5x + 14 = 2(x + 12) + 11

    5x + 14 = 2x + 24 + 11

    5x + 14 = 2x + 35

    5x - 2x = 35 - 14

    3x = 21

    x = 7

    Joe is (5x + 8) yrs old right now, so he is (5(7) + 8) = 35 + 8 = 43 yrs old.

    Check: Six years ago he would have been 43 - 6 = 37

    His daughter was 7 yrs old. So 5(7) + 2 = 37 (looks good)

    Six years from now he will be 49.

    His daughter will be 7 + 6 + 6 = 19.

    11 years more than twice her age would be 2(19) + 11 = 49.

    Hope this helps! You could also have solved this by letting the daughter's age be x right now, and then subtract for 6 years ago. I like to keep things positive, though! :)

  • 1 decade ago

    I love these types of questions. You obviously have to set up a system of equations, but first lets label our variables:

    let x = Joe Foster's current age

    let y = Daughter's current age

    Now lets convert words to eqautions, if Joe Foster WAS two years MORE than 5 TIMES as old as HIS DAUGHTER... Lets stop right there because we can make an equation, notice how I put emphasis on some words, because those words are the words that will help you convert the whole problem to numbers and variables. Joe Foster WAS, that means we can write x =, x goes for foster and the = sign goes for WAS. He was 2 more (we can substitute more for the + sign) years that 5 TIMES as old as HIS DAUGHTER (we can substitute this for 5y). Then the equation is:

    x = 5y + 2

    We made the first equation, now we still have to make another equation. Six years from now ( we can write x + 6 and y + 6 since after six years both their ages will increase by 6) he WILL BE 11 years MORE than twice as old as she will be. If we combine everything the equation we get is:

    (x+6) = 2(y+6) + 11

    Because his age six years from now (x + 6) is equal to 2 times the daughter's age six years from now [2(y + 6)] plus 11 (+11). Now simplify:

    x+6 = 2y + 12 + 11

    x+6 = 2y + 23

    OR

    x = 2y + 17

    We got our second equation, now all we got to do is solve the system (I HOPE YOU KNOW HOW TO DO THAT)

    x = 5y + 2

    x = 2y + 17

    I'm going to use the elimination method by canceling the x's. Multiply the first equation by -1 to get -x so the x's cancel

    -x = -5y - 2

    x = 2y + 17

    X's cancel

    0 = -3y + 15

    Move -3y to the other side and solve for y

    3y = 15

    y = 5

    Now we know that the daughter current age is 5 years old since y = daughter's current age, but we need to know joe's age, simply substitute y for 5 in any equation and solve for x:

    x = 5(5) + 2

    x = 25 + 2

    x = 27

    Joe is 27 years old.

    HOPE THAT HELPED YOU!!!

    You can check everthing too by going back to your question and working backwards, I AM POSITIVELY SURE THAT THIS IS THE ANSWER, THIS IS THE RIGHT ANSWER, I CHECKED. WHY?????? BECAUSE I LOVE TO DO THESE QUESTIONS

  • 1 decade ago

    Let x be his age now. y be his daughter's age now.

    6 yrs ago,

    x - 6 = 5(y - 6) + 2

    6 yrs from now,

    x + 6 = 2(y + 6) + 11

    solve for x with these two simultaneous qns

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