Math  /  Algebra

Question1. A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each.

Studdy Solution

STEP 1

What is this asking? We need to figure out how old a boy and his brother are right now, knowing that the boy is 10 years older than his brother and in 4 years he'll be twice his brother's age. Watch out! Don't mix up the present ages with their ages in 4 years!

STEP 2

1. Set up variables
2. Create equations
3. Solve for the brother's age
4. Solve for the boy's age

STEP 3

Let's call the boy's current age bb and the brother's current age rr.
This makes it easy to remember who is who!

STEP 4

We know the boy is **10 years older** than his brother *right now*.
So, we can write that as an equation: b=r+10b = r + 10.
See how the boy's age (bb) is the brother's age (rr) plus **10**?

STEP 5

In **4 years**, the boy will be b+4b + 4 years old and the brother will be r+4r + 4 years old.
At that time, the boy will be *twice* as old as his brother.
We can write *that* as an equation too: b+4=2(r+4)b + 4 = 2 \cdot (r + 4).

STEP 6

Now for the fun part!
We have two equations and two unknowns.
Let's substitute the first equation (b=r+10b = r + 10) into the second equation: (r+10)+4=2(r+4)(r + 10) + 4 = 2 \cdot (r + 4).
We're replacing the bb in the second equation with the equivalent expression from the first equation.

STEP 7

Let's simplify that equation: r+14=2r+8r + 14 = 2r + 8.
We combined the **10** and **4** on the left, and distributed the **2** on the right.

STEP 8

Now, subtract rr from both sides: 14=r+814 = r + 8.
We're getting closer to finding rr!

STEP 9

Finally, subtract **8** from both sides: 6=r6 = r.
So, the brother's current age is **6**!

STEP 10

Remember our first equation? b=r+10b = r + 10.
Let's plug in the brother's age (r=6r = 6) that we just found: b=6+10b = 6 + 10.

STEP 11

That means b=16b = 16.
The boy's current age is **16**!

STEP 12

The boy is currently **16** years old, and his brother is **6** years old.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord