… 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.

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

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

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).

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?

:)