Quadratic Applications Sp06

Quadratic Applications

1. Find the dimensions of a rectangle with length twice its width and which has a perimeter of 10

inches.

2. If Jack and Jill receive a total of $500 in Christmas gifts and Jill receives $150 more than Jack,

how much does each receive?

3. The UNC Student Store decides to sell a box of UNC Candy which contains 25 pieces of candy

and will cost $12. The box contains some chocolate rams which cost $0.30 each to make and

some white chocolate tarheels which cost $0.45 each to make. If the store wants to make a profit

of $2.85 on each box, how many of each candy should they include?

4. You have a heated argument with your best friend, after which you storm out of his house and

head home on your bike at 15 miles per hour. Your friend waits 5 minutes before he realizes you

are not coming back and he heads out after you on his motorized scooter at a speed of 18 miles per

hour. How far have you traveled when he meets you?

5. At the beginning of the semester you buy a futon at a 15% discount. If you paid $467.50 for it,

what was the original price?

6. A bank loaned out $15,000, part of it at the rate of 7.5% per year and the rest at the rate of 12% per

year. If the interest received totaled $1500 at the end of one year, how much was loaned at 12%?

7. A farmer wants to enclose his gardens to keep the pests out. He has 2 adjacent square gardens that

he wants to put a fence around, but doesn’t need double fencing between the two (see picture

below). If he uses a total of 315 feet to enclose the gardens, what are the dimensions of the

gardens?

8. A fraternity sells apple cider and fried dough at its annual Fall Fest. If they sell 30 total items in

one hour selling the cider for $1.50 per cup and the dough for $2 per item, how many of each have

they sold if they take in a total of $57?

9. A motorboat can maintain a constant speed of 12 miles per hour relative to the water. The boat

makes a trip upstream to a certain point in 40 minutes. The return trip takes 20 minutes. What is

the speed of the current?

10. Suppose you have $16,000 to invest in 2 accounts. You want each account to earn the same

amount of interest at the end of 2 years. If the accounts earn 10% and 12.5% per year, how much

should you invest in each account?

3. 14 rams; 11 tarheels

4. 7.5 miles

5. original price of futon = $550

6. $8333.33 was loaned out at 12%

7. 45 ft by 45 ft

8. 24 fried donuts; 6 cups of apple cider

9. speed of current = 4 m.p.h.

10. $8888.89 at 10% and $7111.11 at 12.5%