Question

Tom's and Tim's ages add up to 21 years. After three years, Tom will be twice Tim’s age. How old are the two boys now?
Tom: 12 years, Tim: 9 years
Tom: 16 years, Tim: 5 years
Tom: 14 years, Tim: 7 years
Tom: 15 years, Tim: 6 years

Answer 1

I think that you problem can be modeled by the subsequent system:
\[\left\{ \begin{gathered}
to + ti = 21 \hfill \\
to + 3 = 2\left( {ti + 3} \right) \hfill \\
\end{gathered} \right.\]

Answer 2

where to is Tom's age, whereas ti is Tim's age

Answer 3

ok

Answer 4

we have to solve it. How many ways do you know for solving an algebraic system?

Answer 5

for this problem i dont know

Answer 6

I rewrite the second equation as below:
\[to + 3 = 2ti + 6\]

Answer 7

then I subtract 3, from both sides, so I get:
\[to = 2ti + 3\]

Answer 8

now, we have to substitute that condition into the first equation,
namely we have to substitute 2ti+3, in place of to into the first equation of our algebraic system, try please, what do you get?

Answer 9

is it 5

Answer 10

what is 5?

Answer 11

hint:
\[to + ti = \left( {2ti + 3} \right) + ti\]

Answer 12

so our first equation, can be rewritten as below:
\[\left( {2ti + 3} \right) + ti = 21\]

Answer 13

please, solve it for "ti"

Answer 14

hint:
next step:
\[\begin{gathered}
2ti + 3 + ti = 21 \hfill \\
3ti + 3 = 21 \hfill \\
\end{gathered} \]

Answer 15

I subtract 3 from both sides, so I get:
\[3ti = 18\]

Answer 16

what is "ti"?

Answer 17

i really dont know

Answer 18

we have to divide both sides by 3, so we get:
\[ti = \frac{{18}}{3} = ...?\]

Answer 19

therefore, the value of "ti" is:
ti=...?

Answer 20

wait is it 15 + 3 = 18

Answer 21

no, ti=6 so to=21-6=...?

Answer 22

15

Answer 23

that's right!

Answer 24

so what is the right option?

Answer 25

d

Answer 26

ok!

Answer 27

thanks can you help with a couple more

Answer 28

yes!

Answer 29

ok