solving systems of equations algebraically *help please*

[cole92]

Okay, I've actually got two problems, one I have solved out but I'm not sure if it is correct:

"A wholesaler is offering two different packages of custom printed T-shirts and sweatshirts. One pack contains 10-dozen t-shirts and 14 dozen sweatshirts for $1544. The other pack contains 18 dozen T-shirts and 8 dozen sweatshirts for $1472. Write and solce a system of linear equations to find the cost, in dollars, of a dozen T-shirts."

I'm not sure if i did this correct so if I am wrong, please let me know how I messed up:

Pkg 1: 14s+10t=1544 ---multiply by 18
Pkg 2: 8s+18t = 1472 --- multiply by 10

Pkg 1: 252s+180t=27792
Pkg 2: 80s + 180t=14720

172s=13072
s=76

8(76)+18t=1472
608+18t=1472
18t=864
t=48

so it cost $48 for a dozen T-shirts?




Question 2:
The average of two numbers is 7. Find the numbers if three times on of the numbers is one-half the other number.

I need to use systems of equations, but I'm not sure how to set it up.



Any help would be great. Thanks!

 

[Loren]

I agree with your first problem, except it would help if you took the time to name stuff, i.e....
Let t represent the cost of one dozen T-shirts.
Let s represent the cost of one dozen sweatshirts.

On the second one, start by naming the numbers you are after.
Let a be one number.
Let b be the other number.

Build one equation on the fact that you find the average of two numbers by adding them together and dividing the sum by 2.
The 2nd equation is probably easy for you to build. If not, show us what you have done so far and we'll try to help.