Six years ago, Joe Foster was two years more than five timesas old as his daught

Question

Six years ago, Joe Foster 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 using a system of two equations in tow variables. show each step and explain. Six years ago, Joe Foster 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 using a system of two equations in tow variables. show each step and explain.

Explanation / Answer

let x = Joe Foster's current age let y = Daughter's current age Now lets convert words to eqautions, if Joe Foster WAS two yearsMORE than 5 TIMES as old as HIS DAUGHTER... Lets stop right therebecause we can make an equation, notice how I put emphasis on somewords, because those words are the words that will help you convertthe whole problem to numbers and variables. Joe Foster WAS, thatmeans we can write x =, x goes for foster and the = sign goes forWAS. He was 2 more (we can substitute more for the + sign) yearsthat 5 TIMES as old as HIS DAUGHTER (we can substitute this for5y). 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 (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, simplysubstitute y for 5 in any equation and solve for x: x = 5(5) + 2 x = 25 + 2 x = 27 Joe is 27 years old.

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