Builder Jacob had 6 times as many bricks as Builder Tim. After Builder Jacob received an additional 400 bricks and Builder Tim an additional 1450, Builder Jacob now has twice as many bricks as Builder Tim. How many bricks did Builder Jacob have at first?

Answer 1

Let's start by using variables to represent the number of bricks each builder had at first.

Let J be the number of bricks that Builder Jacob had at first.
Let T be the number of bricks that Builder Tim had at first.

From the problem statement, we know that:

J = 6T (Builder Jacob had 6 times as many bricks as Builder Tim)

After they both received additional bricks:

J + 400 = 2(T + 1450) (Builder Jacob now has twice as many bricks as Builder Tim)

Now we can use the first equation (J = 6T) to substitute for J in the second equation:

6T + 400 = 2(T + 1450)

Distribute 2:

6T + 400 = 2T + 2900

Subtract 2T from both sides:

4T + 400 = 2900

Subtract 400 from both sides:

4T = 2500

Divide both sides by 4:

T = 625

So Builder Tim had 625 bricks at first.

Now we can use the first equation (J = 6T) to find J:

J = 6T = 6(625) = 3750

Therefore, Builder Jacob had 3750 bricks at first.