April 18, 2016

Three bricklayers and four carpenters earn a total of $910 a day. Ten bricklayers and five carpenters earn …?

… a total of $1850 a day.

a) Set up a system of equations to describe the word problem.
I got: 1) 3b + 4c = 910 and 2) 10b + 5c + 1850.
So 13b + 9c = 2760 or is it -7b + -1c = -940 or 7b + 1c = 940?
b) Is there an advantage to eliminating either variable first? Explain.
I got: Yes, C would be easier to solve for first cause theres only 1 of them
c) Determine the daily wage of a bricklayer.
This one i’m not sure how to answer.

Comments

pull your punches

Let b be the amount earned by a bricklayer and c be the amount earned by the carpenter, then

3b + 4c = 910 and 10b + 5c = 1850

It does not really appear that either variable would give you an advantage unless you reduce the second equation to 2b + c = 370, then it would be easier to eliminate the c.

Using the equations: 3b + 4c = 910 and 2b + c = 370, multiply the second equation by -4 and add the equations

3b + 4c = 910
-8b – 4c = -1480

-5b = -570
b = 114

ralphers

Your equations are correct:
3b + 4c = 910
10b + 5c = 1850.

replacing b with
b= (910 – 4c)/3

10*(910-4c)/3 + 5c = 1850
9100 – 40c + 5c*3 = 1850*3
9100 – 40c + 15c = 5550
9100 – 25c = 5550
25c = 9100-5550 = 3550
c= 3550/25 = 142

them b = (910 – 4 * 142)/3 = (910 – 568)/3 =114

pierced_kitten21

3b+4c=910——-(1)
10b+5c=1850———-(2)
(1)-(2)=>
-7b-c=-940=>
7b+c=940———(3)
(1)+(2)=>
13b+9c=2760——(4)
(4) & (3) are correct, but either
of which does not help to solve
the problem. Yes, it is best to
eliminate a variable first or replace
c of (1) by that of (3),ie.
3b+9(940-7b)=910 & hence solve
for b.
The solution of this system is
b=$114
c=$142
Here b means that each of the
bricklayers earns $114 a day,
therefore is the answer for (c).

patricia e

a)

1) 3b + 4c = 910
2) 10b + 5c = 1850

This is fine!
It would be better if you divided the 2) by 5

3b + 4c = 910
2b + c = 370

so you can solve the second wrt c and plug the result in the first

c = 370 – 2b
3b + 4(370 – 2b) = 910

c = 370 – 2b
3b + 1480 – 8b = 910

5b = 570
b = 114

c = 370 – 2· 114
c = 142

$142 ? 110 EUR
looks like a nice salary!
is it tax excluded?
:)

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