   SEARCH HOME Math Central Quandaries & Queries  Question from karen, a student: on dave's birthday, his brother henry is 17 years younger than 3 times dave's age,. the boys father, tim is 17 years older than twice henry's age if dave is 7 years younger than his brother. how many candles are on dave's birthday cake? We have two responses for you

What we need to do here is first pick out only the information that we need, that is information that will help us calculate Dave's age. Therefore the only information we need is that Henry is 17 years younger than 3 times Dave's age and Dave is 7 years younger than Henry.

Now we need to set up a series of two equation in two variables then solve them by whatever method you prefer, be it elimination, substation, or by setting up and solving an augmented matrix.

The two equations would be based directly on the two statements involving Dave and Henry.

For example: if I were to say that Mary is 5 years older than twice Lacy's age, and I let m represent Mary and l represent Lacy then the equation would be:

m = 2l + 5 or m - 2l = 5

crnl

Hi Karen.

Let D equal Dave's age, H equal Henry's age, and T equal Tim's age.

Now translate the sentences into equations:

"Henry is 17 years younger than 3 times Dave's age": H = 3D - 17

"Tim is 17 years older than twice Henry's age": T = 2H + 17

"Dave is 7 years younger than his brother (Henry)": D = H - 7

"How many candles are on Dave's birthday cake?": Find D.

So solve for D using the elimination and/or the substitution method for simultaneous equations to find D:
H = 3D - 17
T = 17 + 2H
D = H - 7

You can look up those concepts in our Quick Search if you need more help.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.