Solving word problems using a system of equations (i'm guessing simultaneous).

[Daps]

you are laying the yellow and green brick road. the road is 1m wide and each brick is 500mm x 250mm. there are 3yellow bricks for every green brick. the road will be built with 12000 yellow bricks .how long will the road be?

Let x represent the no of yellow bricks
Let y represent the no of green bricks
I managed to get that x=3y-----equation 1
couldn't work equation 2 even though i could infer that y to be 4000bricks.
the 500mm x250mm brick (i'm thinking 8 of them is needed to fit into a square meter.

please can anyone enlighten me.
thanks

 

[skeeter]

you are laying the yellow and green brick road. the road is 1m wide and each brick is 500mm x 250mm. there are 3yellow bricks for every green brick. the road will be built with 12000 yellow bricks .how long will the road be?

Let x represent the no of yellow bricks
Let y represent the no of green bricks
I managed to get that x=3y-----equation 1
couldn't work equation 2 even though i could infer that y to be 4000bricks.
the 500mm x250mm brick (i'm thinking 8 of them is needed to fit into a square meter.

please can anyone enlighten me.
thanks

12000 yellow + 4000 green = 16000 bricks total

8 bricks for every square meter

16000/8 = 2000 square meters = 1 meter x 2000 meters

 

[Daps]

skeeter, thanks for your take on this question.sorry how did you work out they are suppose to have 8 bricks to fit in 1 square meter.

secondly what are the systems of equations (probably 2 equations).needed here.

Thanks replies are welcomed from everybody.

 

[skeeter]

given brick dimensions ...

500mm x 250mm = 0.5 m x 0.25 = 1/2 m x 1/4 m = 1/8 square meter

8 bricks x 1/8 square meter per brick = 1 square metersimultaneous equations? why make it more difficult?

 

[CellCoree]

I would like to clarify that solving word problems using a system of equations is a common mathematical approach, not just limited to simultaneous equations. In this case, we can create two equations based on the given information:

1. The total number of yellow bricks is 12,000: x = 12,000
2. The ratio of yellow to green bricks is 3:1: x = 3y

From these two equations, we can solve for the value of y, which represents the number of green bricks. Substituting the value of x from the first equation into the second equation, we get:

12,000 = 3y
y = 4,000

Therefore, there are 4,000 green bricks and 12,000 yellow bricks, giving a total of 16,000 bricks.

Now, to find the length of the road, we need to convert the measurements to the same unit. Since the width of the road is 1m, we can convert the brick measurements to meters by dividing by 1000.

The yellow brick is 500mm x 250mm = 0.5m x 0.25m
The green brick is 500mm x 250mm = 0.5m x 0.25m

The total length of the road can be calculated by multiplying the number of bricks by their respective lengths:

Total length = (12,000 x 0.5m) + (4,000 x 0.25m)
= 6,000m + 1,000m
= 7,000m

Therefore, the road will be 7,000 meters long.

I hope this explanation helps to clarify the process of solving word problems using a system of equations. If you have any further questions, please feel free to ask. Thank you.