during a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for $85.50. later you return to the same store and but three more sweatshirts and four more pairs of sweatpants for $123. what is the sale price of each sweatshirt and each pair of sweatpants?

3 sweatshirts and 2 sweatpants for 85.50 --> 3x+2y=85.50

3 sweatshirts and 4 sweatpants for 123 --> 3x+4y=123
solve for one of the variables in either equation (in terms of the other variable) and insert the answer into the other equation to get an actual value of the other variable

3x+2y=85.5
3x=85.5-2y
x=(85.5-2y)/3
x=28.5-(2/3)y --> insert the "x" value into the other equation to solve for "y"

3(28.5-(2/3)y)+4y=123
85.5-2y+4y=123
2y=37.5
y=18.75 --> now insert the "y" value into the first equation to get an actual value for "x"

3x+2(18.75)=85.5
3x+37.5=85.5
3x=48
x=16

FINAL ANSWER:(x=16 and y=18.75)

3s + 4p = 123

3s + 2p = 85.5

Subtract second equation from the first.

2p = 37.5

p = 18.75

You should be able to work it from here.

69 +++=21

Ah, the age-old mystery of sweatshirt and sweatpants pricing! Well, let's solve it with a touch of humor, shall we?

Let's give our sweatshirts a name, like Steve, and our sweatpants a name, like Larry.

So, we have Steve (sweatshirt) and Larry (sweatpants). In the first purchase, we bought 3 Steves and 2 Larrys for $85.50. And in the second purchase, we grabbed 3 more Steves and 4 additional Larrys, but this time for $123.

Now, let's do some mathematics gymnastics. If we subtract the two purchases, we'll find out how much the extra 3 Steves and 4 Larrys cost: $123 - $85.50 = $37.50.

Since we bought 3 more Steves and 4 extra Larrys, the cost of each Steve and each Larry is equal. So, we divide the $37.50 by 3+4 (which equals 7), and we get $5.35.

So, each Steve or sweatshirt is $5.35, and each Larry or sweatpants is also $5.35.

Just remember, Steve and Larry might not appreciate being called sweatshirts and sweatpants, but hey, they're inanimate objects, so they'll get over it!

To find the sale price of each sweatshirt and each pair of sweatpants, we will need to set up a system of equations based on the information given.

Let's assume the price of each sweatshirt is "x" dollars and the price of each pair of sweatpants is "y" dollars.

From the first transaction, we know that you bought three sweatshirts and two pairs of sweatpants for $85.50. This can be written as the equation:

3x + 2y = 85.50 ---(Equation 1)

From the second transaction, we know that you bought three more sweatshirts and four more pairs of sweatpants for $123. This can be written as the equation:

3x + 4y = 123 ---(Equation 2)

Now, we have a system of two equations with two unknowns (x and y). We can solve this system of equations using elimination or substitution method to find the values of x and y, which represent the sale prices of sweatshirts and sweatpants, respectively.

Let's use the elimination method to solve this system:

Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of "x" in both equations the same:

(3)(3x + 2y) = (3)(85.50)
(2)(3x + 4y) = (2)(123)

Simplifying these equations, we get:

9x + 6y = 256.50 ---(Equation 3)
6x + 8y = 246 ---(Equation 4)

Now, subtract Equation 4 from Equation 3 to eliminate the "x" term:

(9x + 6y) - (6x + 8y) = 256.50 - 246
9x - 6x + 6y - 8y = 10.50

Simplifying this equation, we get:

3x - 2y = 10.50 ---(Equation 5)

Now, we have a new equation (Equation 5) that relates only "x" and "y". Let's solve this equation:

Multiply Equation 5 by 2:

2(3x - 2y) = 2(10.50)
6x - 4y = 21 ---(Equation 6)

Now, multiply Equation 6 by 3:

3(6x - 4y) = 3(21)
18x - 12y = 63 ---(Equation 7)

Add Equation 7 to Equation 4:

(6x + 8y) + (18x - 12y) = 246 + 63
24x - 4y = 309

Divide both sides of this equation by 4:

6x - y = 77.25 ---(Equation 8)

Now, we have Equation 8, which relates only "x" and "y". Let's solve this equation:

Multiply Equation 8 by 2:

2(6x - y) = 2(77.25)
12x - 2y = 154.50 ---(Equation 9)

Now, add Equation 9 to Equation 5:

(12x - 2y) + (3x - 2y) = 154.50 + 10.50
15x - 4y = 165

Divide both sides of this equation by 1, we get:

15x - 4y = 165 ---(Equation 10)

Now, we have Equation 10, which relates only "x" and "y". Let's solve this equation:

Multiply Equation 10 by 3:

3(15x - 4y) = 3(165)
45x - 12y = 495 ---(Equation 11)

Now, subtract Equation 11 from Equation 7:

(18x - 12y) - (45x - 12y) = 63 - 495
-27x = -432

Divide both sides of this equation by -27:

x = 16

Now, substitute the value of x into any of the earlier equations (Equation 8, for example) to find the value of y:

6x - y = 77.25
6(16) - y = 77.25
96 - y = 77.25
-y = 77.25 - 96
-y = -18.75
y = 18.75

Therefore, the sale price of each sweatshirt is $16 and the sale price of each pair of sweatpants is $18.75.