Thread: equations

6400 bricks have been delivered by the first day of a bricklaying contract subsequently 1600 bricks are delivered daily.
bricklaying commences on the first day and proceeds regularly, the bricklayers use 2400 bricks per day.
write down 2 equations of the form y=mx+c the first in respect of brick delivery, the second of bricklaying.
use these equations to find out how many days after the commencement of contract the bricklayers will have run out of bricks
thanx
jim

Originally Posted by jim49990

6400 bricks have been delivered by the first day of a bricklaying contract subsequently 1600 bricks are delivered daily.
bricklaying commences on the first day and proceeds regularly, the bricklayers use 2400 bricks per day.
write down 2 equations of the form y=mx+c the first in respect of brick delivery, the second of bricklaying.
use these equations to find out how many days after the commencement of contract the bricklayers will have run out of bricks
thanx
jim

Let D be the number of bricks delivered by day d. Then

D=6400+1600(d-1),

or:

D=4800+1600d.

Let L be the number of bricks laid, then:

L=2400d

The brickies run out of bricks when D<=L, so we look for d such that:

4800+1600d=2400d.

Rearrange this to get:

800d=4800,

or d=6.

That is the brickies will have no bricks on hand at the end of day 6.

RonL

Originally Posted by jim49990

6400 bricks have been delivered by the first day of a bricklaying contract subsequently 1600 bricks are delivered daily.
bricklaying commences on the first day and proceeds regularly, the bricklayers use 2400 bricks per day.
write down 2 equations of the form y=mx+c the first in respect of brick delivery, the second of bricklaying.
use these equations to find out how many days after the commencement of contract the bricklayers will have run out of bricks
thanx
jim

With respect to bricks derlivery:
Let y = number of bicks delivered.
And x = number of days from commencement of contract
y = 6400 +(x-1)*1600
y = 6400 +1600x -1600
y = 1600x +4800 --------------------answer.

With respect to bricklaying:
Let z = number of bricks laid.
And x = number of days from commencement of contract.
z = x*2400
z = 2400x ----------------------answer.

The bricks will run out if the delivered equalls the laid, so,
y = z
1600x +4800 = 2400x
4800 = 2400x -1600x
4800 = 800x
x = 4800/800
x = 6 days

Therefore, after 6 days, the bricklayers will run out of bricks. -----answer.

Check:
Delivery in 6 days = 6400 +5(1600) = 14,400 bricks.
Laid in 6 days = 6*2400 = 14,400 bricks.
Therefore, OK.