Forming equations (sales commissions; pay rates)

[Ishy]

I have 2 math problems that I really don't HAVE to do but I won't learn if I don't. I've tried to figure these out for days and I think I'm just plain stuck. I understand the questions and I could solve them on my own but it asks for me to form an equation that can be used to solve the questions and I just can't come up with it. If someone could help me with this and possibly let me know how they came up with it, I would be very grateful.

Form an equation and then solve it to answer each question. Make a table to organize the data.

1. Commissions. A salesman receives a commission of $3 for every pair of dress shoes he sells. He is paid $2 for every pair of athletic shoes he sells. After selling 9 pairs of shoes in a day, his commission was $24. How many pairs of each kind of shoe did he sell that day?

2. Mover's pay scale. A part-time mover's regular pay rate is $60 an hour. If the work involves going up and down stairs, his rate increases to $90 an hour. In one week, he earned $1,380 and worked 20 hours. How many hours did he work at each rate?

Thank you very much for taking a look at this. Have a nice day!

Ishy

 

[jwpaine]

Re: Forming equations

I have 2 math problems that I really don't HAVE to do but I won't learn if I don't.

Good attitude, but showing us at least a little of what you did in attempt to solve this would be best.

1. Commissions. A salesman receives a commission of $3 for every pair of dress shoes he sells. He is paid $2 for every pair of athletic shoes he sells. After selling 9 pairs of shoes in a day, his commission was $24. How many pairs of each kind of shoe did he sell that day?

Let d = dress, a = athletic type shoes.

You have two variables, so you need two equations to solve: thus a system of equations.

we know that his commission is [$24 = 3d + 2a]
we know that he sold 9 shoes that day, so: [d + a = 9]

Setup your system of equations:

{3d + 2a = 24
{d + a = 9

Using substitution method will be faster. You are algebraically solving a system of equations for d and a, such that it's graphical representation is the point of intersection of the two linear equations.

John.

 

[Denis]

Re: Forming equations

1. Commissions. A salesman receives a commission of $3 for every pair of dress shoes he sells. He is paid $2 for every pair of athletic shoes he sells. After selling 9 pairs of shoes in a day, his commission was $24. How many pairs of each kind of shoe did he sell that day?

Hint:
Let d = pairs of dress shoes; then 9 - d = pairs of athletic shoes
3d + 2(9 - d) = 24

2. Mover's pay scale. A part-time mover's regular pay rate is $60 an hour. If the work involves going up and down stairs, his rate increases to $90 an hour. In one week, he earned $1,380 and worked 20 hours. How many hours did he work at each rate?

Hint:
Let r = regular pay hours; then 20 - r = increased pay hours
60r + 90(20 - r) = 1380

You were probably making it more complicated that it is :wink:

 

[Ishy]

Re: Forming equations

1. Commissions. A salesman receives a commission of $3 for every pair of dress shoes he sells. He is paid $2 for every pair of athletic shoes he sells. After selling 9 pairs of shoes in a day, his commission was $24. How many pairs of each kind of shoe did he sell that day?

Hint:
Let d = pairs of dress shoes; then 9 - d = pairs of athletic shoes
3d + 2(9 - d) = 24

2. Mover's pay scale. A part-time mover's regular pay rate is $60 an hour. If the work involves going up and down stairs, his rate increases to $90 an hour. In one week, he earned $1,380 and worked 20 hours. How many hours did he work at each rate?

Hint:
Let r = regular pay hours; then 20 - r = increased pay hours
60r + 90(20 - r) = 1380

Oh wow, that makes so much more sense than what I was trying to do. I was trying to make an equation that would calculate them both at once and I was getting into fractions and everything. The 9-d and 20-r never occurred to me. I was absolutely overcomplicating it to death so thanks a bunch for getting me on the right track. I feel so silly now!

I wanted to do one on my own too and found another similar problem, which reads:

A preschool charges $8 for a child to attend its morning session or $10 to attend the afternoon session. No child can attend both. Thirty children are enrolled in the preschool. If the daily receipts are $264, how many children attend each session?

I came up with:

8m + 10(30 - m) = 264

and after solving that makes 18 morning and 12 afternoon and it works out when I check it too so I think I've got it now. Thanks a lot :mrgreen:

Ishy