Question 1

The smallest angle in a triangle is  as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.

Accepted Answer

The answer of The smallest angle in a triangle is...

Question 2

One side of a triangle is twice the shortest side. The third side is 2 feet more than the shortest side. The perimeter is 22 feet. Find all three sides.

Accepted Answer

The answer of One side of a triangle is twice...

Question 3

A stockbroker has money in three accounts. The interest rates on the three accounts are 8%, 10%, and 12%. If she has twice as much money invested at 10% as she has invested at 8%, three times as much at 12% as she has at 8%, and the total interest for the year is $384, how much is invested at each rate? ( Hint : Let x = the amount invested at 8%.)

Accepted Answer

The answer of A stockbroker has money in three accounts....

Question 4

Travis has a savings account that his parents opened for him. It pays 6% annual interest. His uncle also opened an account for him, but it pays 12% annual interest. If there is $500 more in the account that pays 6%, and the total interest from both accounts is $102, how much money is in each of the accounts?

Accepted Answer

Let x be the amount in the 6% account, then x - 500 is the amount in the 12% account. The equation for total interest is 0.06x + 0.12(x - 500) = 102. Solving this gives x = 900, so $900 is in the 6% account and $400 is in the 12% account.

Question 5

The cost of a long-distance phone call is $0.38 for the first minute and $0.35 for each additional minute. If the total charge for a long-distance call is $6.68, how many minutes was the call?

Accepted Answer

The answer of The cost of a long-distance phone call...

Question 6

Recently, the Texas Junior College Teachers Association annual conference was held in Austin. At that time a taxi ride in Austin was $1.75 for the first  of a mile and $0.25 for each additional  of a mile. Suppose the distance from one of the hotels to one of the western dance clubs in Austin is 13 miles. If the fare meter in the taxi gives the charge for that trip as $8.00, is the meter working correctly?

Accepted Answer

The answer of Recently, the Texas Junior College Teachers Association...

Question 7

One number is five more than twice another. If their sum is decreased by ten, the result is ten. Find the numbers.

Accepted Answer

The answer of One number is five more than twice...

Question 8

Two angles in a triangle are equal and their sum is four times as the third angle in the triangle. What are the measures of each of the three interior angles?

Accepted Answer

The answer of Two angles in a triangle are equal...

Question 9

Recently, the Texas Junior College Teachers Association annual conference was held in Austin. At that time a taxi ride in Austin was $1.25 for the first  of a mile and $0.50 for each additional  of a mile.If the distance from one of the convention hotels to the airport is 8 miles, how much will it cost to take a taxi from that hotel to the airport?

Accepted Answer

The answer of Recently, the Texas Junior College Teachers Association...

Question 10

A right triangle has one  angle. Find the other two angles.

Accepted Answer

The answer of A right triangle has one  angle....

Question 11

Nick and Carla Cole are driving separately from San Luis Obispo, California, to the north shore of Lake Tahoe, a distance of 375 miles. Nick leaves San Luis Obispo at 11:00 AM and averages 55 miles per hour on the drive, Carla leaves later, at 4:00 PM but averages 60 miles per hour. Which person arrives in Lake Tahoe first?

Accepted Answer

We can use the formula:
time = distance / speed
For Nick: 
time = 375 miles / 55 mph = 6.82 hours
For Carla: 
time = 375 miles / 60 mph = 6.25 hours
Nick's departure time is 11:00 AM and Carla's departure time is 4:00 PM, so there is a time difference of 5 hours.
Therefore, Carla's arrival time will be 6.25 hours + 5 hours = 11:15 PM
Nick's arrival time will be 11:00 AM + 6.82 hours = 5:49 PM
Since 5:49 PM is earlier than 11:15 PM, Nick arrives at Lake Tahoe first.

Question 12

In a right triangle, one of the acute angles is eight times as large as the other acute angle. Find the measure of the two acute angles.

Accepted Answer

The answer of In a right triangle, one of the...

Question 13

Tyler has two savings accounts that his grandparents opened for him. The two accounts pay 12% and 18% in annual interest; there is $400 more in the account that pays 18% than there is in the other account. If the total interest for a year is $252, how much money does he have in each account?

Accepted Answer

If x is the amount in the 12% account, then x + 400 is the amount in the 18% account. The equation for total interest is 0.12x + 0.18(x + 400) = 252. Solving this gives x = 600, so $600 is in the 12% account and $1,000 is in the 18% account.

Question 14

An accountant has money in three accounts that pay 8%, 10%, and 13% in annual interest. He has twice as much invested at 8% as he does at 10% and three times as much invested at 13% as he does at 10%. If the total interest from the three accounts if $455 for the year, how much is invested at each rate? ( Hint : Let x = the amount invested at 10%.)

Accepted Answer

Let x be the amount invested at 10%. Then, 2x is invested at 8%, and 3x is invested at 13%. The total interest is $455, so the equation is 0.08(2x) + 0.10(x) + 0.13(3x) = 455. Solving this equation gives x = $700, so 2x = $1,400 at 8%, and 3x = $2,100 at 13%.

Question 15

JoAnn works in the publicity office at the state university. She is paid $14 an hour for the first 31 hours she works each week and $20 an hour for every hour after that. If she makes $594 one week, how many hours did she work?

Accepted Answer

The answer of JoAnn works in the publicity office at...

Question 16

One number is three less than another. Their sum is five. Find both numbers.

Accepted Answer

The answer of One number is three less than another....

Question 17

One angle in a triangle measures twice the smallest angle, whereas the largest angle is six times the smallest angle. Find the measures of all three angles.

Accepted Answer

The answer of One angle in a triangle measures twice...

Question 18

One number is three more than another. Their sum is seven. Find both numbers.

Accepted Answer

The answer of One number is three more than another....

Question 19

Miguel is selling tickets to a barbeque. The tickets are $5.50 for adults and $4.50 for children. He sells twice as many adult tickets as children's tickets and brings in a total of $93.00. How many of each kind of ticket did he sell?

Accepted Answer

The answer of Miguel is selling tickets to a barbeque....

Question 20

Tyler is taking piano lessons. Because he doesn't practice as often as his parents would like him to, he has to pay for part of the lessons himself. His parents pay him $0.75 to do the laundry and $1.25 to mow the lawn. In one month, he does the laundry 6 more times than he mows the lawn. If his parents pay him $16.50 that month, how many times did he mow the lawn?

Accepted Answer

Let's denote the number of times Tyler mows the lawn as "x". Then, the number of times he does the laundry is "x+6" (as he does laundry 6 more times than mowing the lawn).

The amount of money Tyler earns from doing laundry is:
$0.75(x+6) = $0.75x + $4.50

The amount of money Tyler earns from mowing the lawn is:
$1.25x

Together, these add up to the total amount Tyler earns in a month:
$0.75x + $4.50 + $1.25x = $16.50

Simplifying this equation, we get:
$2.00x + $4.50 = $16.50
$2.00x = $12.00
x = 6

Therefore, Tyler mows the lawn 6 times (as we initially denoted with "x"), which is answer choice B.

Quiz 2: Simplifying Expressions

The smallest angle in a triangle is as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.