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 startfraction one-third endfraction of the short-sleeved shirts and startfraction one-half endfraction of the long-sleeved shirts, for a total of 100 shirts.
this system of equations models the situation.
5x + 10y = 1,750
x + a system of equations. 5 x plus 10 y equals 1,750. startfraction one-third endfraction x plus startfraction one-half endfraction y equals 100.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?

The drama club ordered 150 short-sleeved shirts and 100 long-sleeved shirts

Step-by-step explanation:

1. Let's review all the information provided for answering the questions properly:

5x + 10y = 1,750

1/3x + 1/2y = 100

x = number of short-sleeved shirts ordered

y = number of long-sleeved shirts ordered

Resolving the 1st equation:

5x + 10y = 1,750

5x = 1,750 - 10y

x = 350 - 2y (Dividing by 5 at both sides)

Resolving  the 2nd equation:

1/3x + 1/2y = 100

1/3 (350 - 2y) + 1/2y = 100

350/3 -2y/3 + 1/2y = 100

700 - 4y + 3y = 600 (Lowest common denominator = 6)

-y = 600 - 700 (Subtracting 700 at both sides)

y = 100 (Dividing by - 1)

Finding the value of x in the 1st equation:

5x + 10 (100) = 1,750

5x + 1,000 = 1,750

5x = 1,750 - 1,000 (Subtracting 1,000 at both sides)

5x = 750

x = 150 (Dividing by 5)

2. Proving that x = 150 and y = 100 are correct

1/3x + 1/2y = 100

1/3 * 150 + 1/2 * 100 = 100

150/3 + 100/2 = 100

50 + 50 = 100

100 = 100

We proved that x = 150 and y = 100 are correct

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