Question

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold of the short-sleeved shirts and of the long-sleeved shirts, for a total of 100 shirts. This system of equations models the situation. 5x + 10y = 1,750 x + y = 100 Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. How many short-sleeved shirts were ordered? How many long-sleeved shirts were ordered?

Answer 1

5x+10y=1750
x+y=100

Multiply the second equation by -5 and add
5y=1250, so y=250
Plugging that back in, we get that x=-150, but that doesn't make sense, so it's either that they sold negative short sleeved shirts or didn't reach their goal of 1750 dollars

Answer 2

Which is not possible since no shirt cannot be in negative in number.

Explanation:

x+y =100....................... eq(1)

5x +10y =1,750..................eq(2)

Dividing equation 2 by 5 ,we get

x+2y = 350 ....................eq(3)

x+y =100

we get y=100-x from equation(1) and plugging it in equation (3)

x+2(100-x) =350

x+200-2x =350

-x = 350-200

-x = 150

=-150

which is not possible since x( number of shirts) cannot be negative.