Six years aago, Tom JOnes was two years more than five timesas old as his daught

Question

Six years aago, Tom JOnes was two years more than five timesas old as his daughter. Six years from now, he will be 11years more than twice as old as she will be. How old isJoe? solve by using a system of two equations in twovariables. Show and explain each step. Six years aago, Tom JOnes was two years more than five timesas old as his daughter. Six years from now, he will be 11years more than twice as old as she will be. How old isJoe? solve by using a system of two equations in twovariables. Show and explain each step.

Explanation / Answer

Who's Joe? Assuming you meant Tom, here's how you woulddo it: let x = Tom Jones current age
let y = Daughter's current age

Now lets convert words to eqautions, if Tom Jones WAS twoyears MORE than 5 TIMES as old as HIS DAUGHTER... Lets stop rightthere because we can make an equation, notice how I put emphasis onsome words, because those words are the words that will help youconvert the whole problem to numbers and variables. TomJones WAS, that means we can write x =, x goes for Tomand the = sign goes for WAS. He was 2 more (we can substitute morefor the + sign) years that 5 TIMES as old as HIS DAUGHTER (we cansubstitute this for 5y). Then the equation is:

x = 5y + 2

We made the first equation, now we still have to make anotherequation. Six years from now ( we can write x + 6 and y + 6 sinceafter six years both their ages will increase by 6) he WILL BE 11years MORE than twice as old as she will be. If we combineeverything 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 thedaughter's age six years from now [2(y + 6)] plus 11 (+11). Nowsimplify:

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 thesystem:

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 Tom's age, simplysubstitute y for 5 in any equation and solve for x:

x = 5(5) + 2
x = 25 + 2
x = 27

Tom is 27 years old.

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