Simultaneous equations in word form (2)

[CSmith1]

The wage bill for six women and five men is \$670. The bill for eight men and three women is \$610. Find the wages of (1) a man and (b) a woman.

i set it up like this :

6x+5y=670
3x+8y=610

did i set it up right because word questions confuses me .

 

[MarkFL]

Yes, you have set it up correctly.

 

[CaptainBlack]

The wage bill for six women and five men is \$670. The bill for eight men and three women is \$610. Find the wages of (1) a man and (b) a woman.

i set it up like this :

6x+5y=670
3x+8y=610

did i set it up right because word questions confuses me .

When setting up the equations you might find it more intuitive to use m and w for the wages of men and women repetitively (you should also at a minimum say what each variable represents).

CB

 

[HallsofIvy]

Unfortunately, this problem assumes, without saying so, that all men make the same wage and that all women make the same wage. That seems silly to me.

 

[CellCoree]

Yes, you have set up the equations correctly. The first equation represents the wage bill for six women and five men, where x represents the wage for a woman and y represents the wage for a man. The second equation represents the wage bill for eight men and three women. To solve for the wages of a man and a woman, you can use the substitution method or the elimination method. In this case, using the substitution method would be easier.

From the first equation, we can rearrange it to solve for y: y = (670-6x)/5

Substituting this value of y into the second equation, we get:

3x + 8((670-6x)/5) = 610

Simplifying this equation, we get:

3x + 1072 - 48x = 3050

-45x = 1978

x = -43.96

This means that the wage for a woman is approximately \$43.96.

To find the wage for a man, we can substitute this value of x into the first equation:

6(-43.96) + 5y = 670

-263.76 + 5y = 670

5y = 933.76

y = 186.75

Therefore, the wage for a man is approximately \$186.75.

Note: In real-world scenarios, wages are usually rounded to the nearest dollar, so the actual wages may differ slightly from the calculated values.