Arithmetic
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ACT Math › Arithmetic
A new car can travel an average of 63 miles per gallon of gasoline. Gasoline costs $5.05 per gallon. How much would it cost to travel 6,363 miles in this car?
$505
$101
$405.05
$510
$510.05
Explanation
First, find the total amount of gas necessary for the trip. 6363/63 = 101 gallons (easy to see as 63 * 100 = 6300 + 1 * 63 = 6363). Then multiply the number of gallons by the price per gallon of gasoline, 5.05 * 101 = $510.05 and is your answer (again, easy to see when 5.05 * 100 + 1 * 5.05).
The largest of three numbers is six less than four times the smallest number. The middle number is three more than twice the smallest number. The sum of twice the largest number, three more than three times the middle number, and four times the smallest number is 90. What is the value of the largest number?
14
10
12
18
22
Explanation
Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.
2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5
4(6)-6 = 14
76 eleventh-grade students turned in term papers on the United States Constitution. 3 students failed, 26 students recieved C's, 31 students recieved B's. The remaining students earned A's on their papers.
What percentage of students earned A's on their paper? (Round to the nearest percent.)
Explanation
Subtract 3, 26, and 31 from 76 to figure out how many students got A's (16).
What is the probability of selecting a prime number out of the following set?
{2, 6, 9, 17, 21, 47, 63, 71, 81}
3/9
4/9
5/9
6/9
9/4
Explanation
Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.
Evaluate:
–1 + 2 * –3
–3
5
–7
7
3
Explanation
First you perform multiplication 2 * –3 = –6
Then you add –1 which gives you -7.
Evaluate:
–1 + 2 * –3
–3
5
–7
7
3
Explanation
First you perform multiplication 2 * –3 = –6
Then you add –1 which gives you -7.
What is the probability of selecting a prime number out of the following set?
{2, 6, 9, 17, 21, 47, 63, 71, 81}
3/9
4/9
5/9
6/9
9/4
Explanation
Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.
Which of the following fractions is equivalent to
Explanation
To convert an integer percentage into an improper fraction, set the percentage as a fraction over 
Find the sum of the following:
Explanation
To get the decimal from a fraction, divide the numerator by the denominator
The largest of three numbers is six less than four times the smallest number. The middle number is three more than twice the smallest number. The sum of twice the largest number, three more than three times the middle number, and four times the smallest number is 90. What is the value of the largest number?
14
10
12
18
22
Explanation
Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.
2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5
4(6)-6 = 14