Question

In 5 years kate will be twice as old as joey. right now kate is 11 years older then joey. right now how old is joey?

Answer 1

K = Kate's age nowJ = Joey's age nowK+5 = Kate's age in 5 yearsJ+5 = Joey's age in 5 years From the first sentenceK+5 = 2(J+5) From the second sentenceK=J+11 So our system of equations isK+5 = 2(J+5)K=J+11 The first equation is equivalent toK+5 = 2J+10or by rearranging termsK-2J=5  The second equation is equivalent toK-J=11 This gives us K-2J=5K-J=11 Using the elimination method, we need to multiply one of the equations by a factor such that we can eliminate one of the variables.  This means we want one of the variables to have coefficients which are the same magnitude but opposite signs.  We can do this by multiplying the 1st equation by -1.  This give us -K+2J=-5 K - J = 11 Now add these two equations together, term by term.  This gives usJ=6 So Joey is 6 years old now.