1. ## Find Combined Cost

Three shirts and 2 neckties cost $69. At the same prices, 2 shirts and 3 neckties cost$61. What is the combined cost of one shirt and one necktie?

I realize this is a system of linear equations in 2 variables.

Let s = shirts and n = neckties

I came up with the following two equations:

3s + 2n = 69
2s + 3n = 61

Is this right so far?

I came up with a combined cost of $35. The right answer is$26. What did I do wrong?
How do I get $26? 2. Hallo mangentarita! Originally Posted by magentarita Three shirts and 2 neckties cost$69. At the same prices, 2 shirts and 3 neckties cost $61. What is the combined cost of one shirt and one necktie? I realize this is a system of linear equations in 2 variables. Okay. Originally Posted by magentarita Let s = shirts and n = neckties Well, s = price of one shirt and n = price of one necktie. Originally Posted by magentarita I came up with the following two equations: 3s + 2n = 69 2s + 3n = 61 Is this right so far? Yes, it is. Originally Posted by magentarita I came up with a combined cost of$35.

The right answer is $26. What did I do wrong? I don't know. Misscalculation? The equations 3s + 2n = 69 2s + 3n = 61 are solved by n=$9 and s = $17 Originally Posted by magentarita How do I get$26?
9+17 = 26

You failed in solving the two equations

Try again?

Regards, Rapha

3. Hello, magentarita!

Three shirts and 2 neckties cost $69. At the same prices, 2 shirts and 3 neckties cost$61.
What is the combined cost of one shirt and one necktie?

I realize this is a system of linear equations in 2 variables.

Let $\displaystyle s$ = shirts and $\displaystyle n$ = neckties

I came up with the following two equations: .$\displaystyle \begin{array}{ccc}3s + 2n &=& 69 \\ 2s + 3n &=& 61 \end{array}$

Is this right so far? . Yes, good work!
It's hard to see your work from here,
. . but it looks you played the $\displaystyle 8\heartsuit$ instead of the $\displaystyle K\spadesuit.$

But seriously, there is a back-door solution to this problem.

Add the two equations: .$\displaystyle 5s + 5n \:=\:130$

. . Therefore: .$\displaystyle \boxed{s + n \:=\:26}$

4. ## ok...

Originally Posted by Rapha
Hallo mangentarita!

Okay.

Well, s = price of one shirt and n = price of one necktie.

Yes, it is.

I don't know. Misscalculation?

The equations
3s + 2n = 69
2s + 3n = 61

are solved by n=$9 and s =$17

9+17 = 26

You failed in solving the two equations

Try again?

Regards, Rapha
I thank you. I got the wrong answer for n. I somehow got n = 18.

5. ## ok...

Originally Posted by Soroban
Hello, magentarita!

It's hard to see your work from here,
. . but it looks you played the $\displaystyle 8\heartsuit$ instead of the $\displaystyle K\spadesuit.$

But seriously, there is a back-door solution to this problem.

Add the two equations: .$\displaystyle 5s + 5n \:=\:130$

. . Therefore: .$\displaystyle \boxed{s + n \:=\:26}$
I miss your replies. Thank you. How have you been?