Dylan is 219 years old. Guadalupe is 31 years old. How many years until Dylan’s age is 5 times Guadalupe’s age?

Question

Dylan is 219 years old. Guadalupe is 31 years old. How many years until Dylan’s age is 5 times Guadalupe’s age?

Answer 1

We can organize the given info in a chart:

To get the age X years later, add X to the current age.

      Age Today                   Age X years later

|--------------------------------------------------------------|

D |       219                   |          219 + X                   |

|--------------------------------------------------------------|

G |          31                   |          31 + X                    |

|--------------------------------------------------------------|

(I have a colorful chart, but wasn’t able to paste here)

Dylan's age is 5 times Guadalupe's age becomes:

D = 5G

Plug in values from the chart:

219 + X = 5(31 + X)



Solve for X:

219 + X = 5*31 + 5*X

219 + X = 155 + 5*X

219 = 155 + 4*X

64 = 4*X

X = 16 Answer

Answer 2

If Dylan (D) is 219 and Guadalupe (G) is 31, and we are looking for when D is 5x G's age, start with writing an equation of what we NEED:

D_future = 5*G_future (we need D's age to be 5 times G's age)

Right now, D_current = 219 and G_current = 31. We know we cant plus the current ages in the above statement, because the equality wouldn't hold. To get from the current age, to a future age where the equality holds, we will add X. Sometime in the future, say X years, D will be 5 times the age of G. Write the formula that would make the statement true.

D_future = 5*G_future (first equation of what we need)

(D_current + X) = 5 * (G_current + X) --> adding X years to both people's current age

(219 + X) = 5 * (31 + X) --> we know D_current and G_current

Now, you have 1 equation, and 1 unknown. Solve for X.

219 + X = 5*31 + 5*X --> distribute the 5

219 + X = 155 + 5*X

219 = 155 + 4*X

64 = 4*X

16 = X

In 16 years, D will be 5x G's age.

Check:

219+16 = 235 (D's age in 16 years)

31+16 = 47 (G's age in 16 years)

47*5 = 235. √