1.A bank teller has a total of 76 bills in five-, ten-, and twenty-dollar denominations. The total value of the money is $890.

(a) Find the total number of solutions. Let x be the number of five-dollar bills, y be the number of ten-dollar bills, and z be the number of twenty dollar bills. Translate the given information into two equations, using x, y, and z as the variables.(Do not factor. Use integers or decimals for any numbers in the expressions.)

(b) Find the solution with the smallest number of five-dollar bills. (c) Find the solution with the largest number of five-dollar bills.

2.An investment of $135,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 9990. The interest from the first investment was 2 times the interest from the second. Find the amounts of the three parts of the investment.The club invested $?at 8%, $?at 6%, and $?at 9%.

3.A company is upgrading office technology by purchasing inkjet printers, LCD monitors, and additional memory chips. The total number of pieces of hardware purchased is 44. The cost of each inkjet printer is $105, the cost of each LCD monitor is $128, and the cost of each memory chip is $85. The total amount of money spent on new hardware came to $4416. They purchased two times as many memory chips as they did LCD monitors. Determine the number of each that was purchased.The company purchased #?inkjet printers,#?LCD monitors, and #?memory chips.(Simplify your answers.)

4.A furniture factory has 2600 machine hours available each week in the cutting department, 1000 hours in the assembly department, and 2360 in the finishing department. Manufacturing a chair requires 0.7 hour of cutting, 0.3 hour of assembly, and 0.4 hour of finishing. A cabinet requires 0.1 hour of cutting, 0.2 hour of assembly, and 0.3 hour of finishing. A buffet requires 0.8 hour of cutting, 0.1 hour of assembly, and 0.7 hour of finishing. How many chairs, cabinets, and buffets should be produced in order to use all the available production capacity?The furniture company should produce #?chairs,#?cabinets, and #?buffets.

5.A rental truck company plans to spend $13 million on 320 new vehicles. Each commercial van will cost $25,000, each small truck $50,000, and each large truck $80,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? They can buy #?vans,#?small trucks, and #?large trucks.(Simplify your answers.)

6.To get the necessary funds for a planned expansion, a small company took out three loans totaling $25,000. Company owners were able to get interest rates of 9%, 10%, and 11%. They borrowed $1000 more at 10% than they borrowed at 11%. The total annual interest on the loans was $2440.The company borrowed $?at 9%, $?at 10%, and $?at 11%.

7.A manufacturer purchases a part for use at both of its plants-one at Roseville, California, the other at Akron, Ohio. The part is available in limited quantities from two suppliers. Each supplier has 95 units available. The Roseville plant needs 40 units, and the Akron plant requires 95 units. The first supplier charges $60 per unit delivered to Roseville and $70 per unit delivered to Akron. Corresponding costs from the second supplier are $90 and $130. The manufacturer wants to order a total of 95 units from the first, less expensive supplier, with the remaining 40 units to come from the second supplier. If the company spends $11,450 to purchase the required number of units for the two plants, find the number of units that should be sent from each supplier to each plant.The first supplier should send #?units to Roseville and #?units to Akron. The second supplier should send #?units to Roseville and #?units to Akron. (Simplify your answers.)

8.A company produces four combinations of mixed vegetables that sell in 1-kg packages. Italian style combines 0.3 kg of zucchini, 0.3 of broccoli, and 0.4 of carrots. French style combines 0.3 kg of broccoli, 0.3 of carrots, and 0.4 of cauliflower. Oriental style combines 0.3 kg of zucchini, 0.2 of broccoli, 0.3 of carrots, and 0.2 of cauliflower. The Combo style combines 0.5 kg of broccoli and 0.5 kg of cauliflower. The company has a stock of 22,200 kg of zucchini, 31,100 kg of broccoli, 27 comma 000 kg of carrots, and 27 comma 700 kg of cauliflower. How many packages of each style should it prepare to use up existing supplies?The company should prepare nothing packages of Italian style,#?packages of French style,#?packages of Oriental style, and #?packages of Combo style.(Simplify your answers.)

9.There are 95 toys to be given out to a group of children. A ball costs $2, a doll costs $3 and a car costs $4. A total of $279was spent on the toys.

There were #?ball(s),#?doll(s), and #?car(s).