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?
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.
Let's solve this step-by-step.
Let's assume the number of bricks Builder Tim had initially was 'x'.
According to the given information, Builder Jacob had 6 times as many bricks as Builder Tim, so Jacob had 6x bricks initially.
After Builder Jacob received an additional 400 bricks, the total number of bricks Jacob had became 6x + 400.
Similarly, after Builder Tim received an additional 1450 bricks, the total number of bricks Tim had became x + 1450.
Given that Jacob now has twice as many bricks as Tim, we can write the equation:
6x + 400 = 2(x + 1450)
Now let's solve this equation for 'x':
6x + 400 = 2x + 2900
Subtracting 2x from both sides:
4x + 400 = 2900
Subtracting 400 from both sides:
4x = 2500
Dividing both sides by 4:
x = 625
Therefore, Builder Tim had initially 625 bricks.
Now let's calculate how many bricks Builder Jacob had initially:
Jacob had 6 times as many bricks as Tim, so:
6x = 6 * 625 = 3750
Therefore, Builder Jacob had initially 3750 bricks.