Kate is 17 years old, and Victor is 12 years younger. In how many years will Kate be twice as old as Victor?

Accepted Solution

Answer:In 7 yearsStep-by-step explanation:Let n ----> the number of yearsx -----> Kate's agey ----> Victor's agewe know that[tex](x+n)=2(y+n)[/tex]we have[tex]x=17\\y=17-12=5\\[/tex]Victor's age is 5substitute the given values[tex](17+n)=2(5+n)[/tex]Solve for n[tex]17+n=10+2n[/tex][tex]2n-n=17-10[/tex][tex]n=7[/tex]VerifyIn 7 yearsKate's age is 17+7=24Victor's age is 5+7=1224=2(12)soKate is twice as old as Victor