Answer:
<u>The drama club ordered 150 short-sleeved shirts and 100 long-sleeved shirts</u>
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)
<u>y = 100</u> (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
<u>x = 150</u> (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
<u>We proved that x = 150 and y = 100 are correct</u>
