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 = 1,750x + 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 = 100Let 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?
Accepted Solution
A:
Answer:150 short-sleeved shirts100 long-sleeved shirtsStep-by-step explanation:Let S and L represent the numbers of short- and long-sleeved shirts ordered.The expected earnings were ... 5S +10L = 1750The number sold was ... (1/3)S + (1/2)L = 100We can multiply the first equation by 1/5 and the second equation by 6 to put the equations into standard form:S +2L = 3502S +3L = 600Subtracting the second equation from twice the first gives ... 2(S +2L) -(2S +3L) = 2(350) -(600) L = 100 . . . . . . simplify 2S +3(100) = 600 S = 150150 short-sleeved and 100 long-sleeved shirts were ordered.