Question 1: A school's band members raised money by selling magazine subscriptions and shirts. Their profit from selling shirts was per shirt minus a one-time set-up fee. Their profit from selling magazine subscriptions was per subscription. They made exactly the same profit from shirts as they did from magazines. They also sold the same number of shirts as magazine subscriptions. How many shirts did they sell?

let x equal the number of shirts they sold.

let x also equal the number of subscriptions they sold, since they sold the same amount of shirts as subscriptions.

the profit on the shirts is 5x - 20.

5x is the profit per shirt.

20 is the one time set up free.

the profit on the subscriptions is 4x.

there is no set up fee.

if the profit is the same, then 5x - 20 = 4x.

solve for x to get x = 20

when they sell 20 shirts, their profit is 5*20 - 20 = 80.

when they sell 20 subscriptions, their profit is 4 * 20 = 80.

same number of shorts sold as subscriptions.

same profit from each.

let x equal the number of shirts they sold.

let x also equal the number of subscriptions they sold, since they sold the same amount of shirts as subscriptions.

the profit on the shirts is 5x - 20.

5x is the profit per shirt.

20 is the one time set up free.

the profit on the subscriptions is 4x.

there is no set up fee.

if the profit is the same, then 5x - 20 = 4x.

solve for x to get x = 20

when they sell 20 shirts, their profit is 5*20 - 20 = 80.

when they sell 20 subscriptions, their profit is 4 * 20 = 80.

same number of shorts sold as subscriptions.

same profit from each.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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step-by-step explanation: