A grocery clerk put only packages of flour tortillas and packages of corn tortillas on a shelf. The ratio of the number of flour tortillas to the number of packages on the shelf was 5 to 9. Which number could be the number of packages of corn tortillas the clerk put on the shelf?
Responses
A 3232
B 1818
C 2323
D 1414
Let's call the number of packages of flour tortillas "5x" and the number of packages of corn tortillas "9x". The total number of packages on the shelf would be 5x + 9x = 14x.
To check which answer choice could be the number of packages of corn tortillas, we need to make sure that it can be expressed as 9x for some value of x. Let's try each answer choice:
A) 32 cannot be divided by 9, so it cannot be the number of packages of corn tortillas. Eliminate A.
B) 18 can be expressed as 2 x 9, so it could be the number of packages of corn tortillas. Keep B as a possibility.
C) 23 cannot be divided by 9, so it cannot be the number of packages of corn tortillas. Eliminate C.
D) 14 cannot be divided by 9, so it cannot be the number of packages of corn tortillas. Eliminate D.
Therefore, the answer is B, 18 packages of corn tortillas.
The list shows the numbers of employees in the seven departments at a company.
14, 23, 54, 30, 26, 17, 26
What is the range of the numbers of employees in these departments?
Responses
A 4040
B 6868
C 99
D 12
The range is the difference between the largest and smallest numbers in the list. To find the largest and smallest numbers, we can simply look for them in the list.
Smallest number: 14
Largest number: 54
Range = Largest number - Smallest number = 54 - 14 = 40
Therefore, the range of the numbers of employees in these departments is 40. Answer choice D is closest to 40, so the answer is D, 12.
what is the value of 5/6 divided by 15/16
Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped upside down). So, to solve 5/6 ÷ 15/16, we can rewrite it as 5/6 x 16/15 (flipping the second fraction to its reciprocal).
Now we can simplify by canceling common factors between the numerator of one fraction and the denominator of the other:
5 and 15 both have a factor of 5, so we can simplify 5/15 to 1/3.
6 and 16 both have a factor of 2, so we can simplify 6/16 to 3/8.
This gives us:
5/6 ÷ 15/16 = 5/6 x 16/15 = (5/3) x (8/15) = 40/45 = 8/9
Therefore, the value of 5/6 divided by 15/16 is 8/9.
On Tuesday 27% of the customers who bought gas at a gas station made additional purchases. There were 300 customers who bought gas. How many of these 300 customers made additional purchases?
Responses
A 8181
B 2727
C 219219
D 273273
To solve the problem, we can start by finding what 27% of 300 is, since 27% represents the proportion of customers who made additional purchases.
27% of 300 can be found by multiplying 0.27 (the decimal equivalent of 27%) by 300:
0.27 x 300 = 81
So, we know that 81 out of the 300 customers made additional purchases.
Therefore, the answer is A, 81.
Reggie writes the expression m + 8 × (2/3). Which expression is equivalent to the one Reggie writes?
Responses
A m + (8×3 ÷ 2)m + (8×3 ÷ 2)
B 8 + m(2 ÷ 3)8 + m(2 ÷ 3)
C (8×2 ÷ 3) + m(8×2 ÷ 3) + m
D (m+8)(2 ÷ 3)
Using the order of operations (PEMDAS), we first need to simplify 8 × (2/3), which equals (8 × 2) ÷ 3 = 16 ÷ 3.
So Reggie's expression simplifies to m + 16/3.
Looking at the answer choices, the only expression that is equivalent to this is option B:
m + (2/3)8 = m + (16/3)
Therefore, the answer is B, 8 + m(2 ÷ 3).
The area of a rectangle is 55.5 square inches. The height of the rectangle is 15 inches. What is the length of the base of the rectangle in inches?
Responses
A 3.7 in3.7 in
B 40.5 in40.5 in
C 832.5 in832.5 in
D 6.5 in