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Question 86433: 6.4
Part I. Use two variables and two equations to set up each problem. Do not solve.
1. One integer is twice another and their sum is 96. Find the integers.
2. The sum of two integers is 38 and their difference is 12. Find the integers.
3. Three times one integer plus another integer is 29. If the first integer plus twice the
second is 18, find the integers.
4. Twice one integer plus another integer is 21. If the first integer plus 3 times the
second is 33, find the integers.
Part II. Use two variables and two equations for each problem. Solve the systems by any method you choose, and write the answer in the appropriate form.
5. A rancher raises five times as many cows as horses. If he has 168 animals, how
many cows does he have?
6. A landscaper used 100 pounds of grass seed containing twice as much bluegrass
as rye. He added 15 more pounds of bluegrass to the mixture before seeding a
lawn. How many pounds of bluegrass did he use?
7. A youth group with 26 members is going skiing. Each of the five chaperones will
drive a van or a sedan. The vans can seat seven people, and the sedans can seat five
people. How many of each type of vehicle could transport all 31 people to the ski
area in one trip?
8. In a mayoral election, the incumbent received 25% more votes than the opponent.
Altogether, 5175 votes were cast for the two candidates. How many votes did the
incumbent mayor receive?
9. The drama club at Lincoln High School sells hot chocolate, and coffee at the
school’s football games to make money for a special trip. At one game, they sold
$200 worth of hot drinks. They need to report how many of each type of drink
they sold for their club records. Macha knows that they used 295 cups that night.
If hot chocolate sells for $0.75 and coffee sells for $0.50, how many of each type
of hot drinks did they sell?
10. Suppose Rent-A-Truck’s rates are $50 a day plus $0.50 per mile and Sam’s U-Drive’s
are $70 a day plus $0.45 a mile.
a. Find the mileage at which the cost for the two would be the same.
b. What is the cost?
c. Under what conditions should one rent from Rent-A-Truck?
11. To earn money for college, Susan is making and selling earrings. Her weekly costs
for advertising and phone calls are $36, and each pair of earrings costs $1.50 to
produce. If Susan sells the earrings for $6 per pair, how many pairs must she sell
per week to break even?
12. Rebecca is the star forward on her high-school basketball team. In one game, her
field-goal total was 23 points, made up of 2-point and 3-point baskets. If she made
4 more 2-point baskets than 3-point baskets, how many of each type of basket did
she make?
13. When Dale baby-sat for 8 hours and worked at a restaurant for 3 hours, he made a
total of $58. When he baby-sat for 2 hours and worked at a restaurant for 5 hours,
he made a total of $40. How much does Dale get paid for each type of work?
14. Beth has saved $4500. She would like to earn $250 per year by investing her money.
She received advice about two different investments; a low-risk investment that
pays a 5% annual interest and a high-risk investment that pays a 9% annual interest.
a. How much should Beth invest in each type of investment to earn her annual
goal?
b. How much should Beth invest in each type of investment if she wishes to
earn $325 per year?
15. The perimeter of a rectangular picture is 86 inches. Twice the width exceeds the
length by 2 inches. What are the dimensions of the picture?
16. The steel braces for a new bridge are in the shape of a right triangle. The hypotenuse
is 75 meters. The length of one leg is four times one-third of the length of the other
leg. Find the lengths of the legs.
17. Maggie is 12 years old and Dwayne is 16. How many years ago was Dwayne five
times as old as Maggie? How old were they at that time?
18. The sum of three numbers is -4. The second number decreased by the third is equal
to the first. The sum of the first and second number is -5. Find the numbers.
6.2
16. The sum of three numbers is 20. The first number is the sum of the second and the third. The third number is three times the first. What are the three numbers?
17. Melissa works at Angela’s Pizza. Her last three orders were 5 slices of pizza, 2 salads and 2 sodas for $9.75; 3 slices of pizza, 2 salads, and 1 soda for $7.15; and 2 slices of pizza, 1 salad, and 1 soda for a total of $4.35. What are the individual prices for pizza, salad, and soda at Angela’s?
Answer by ordy(1)   (Show Source):
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