mathcounts

Two apples, five bananas, and one carrot cost a total of $2.05. Three apples, one banana and four carrots cost a total of $1.89. Three apples, two bananas, and 3 carrots cost a total of $1.98. What is the total cost, in cents, of one apple, one banana, and one carrot?

(a)  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

The numerator of a fraction is 8 less than the denominator. If the numerator is doubled and the denominator is decreased by 1, the value of the resulting fraction is 1. What is the original fraction? Express your answer as a common fraction.

(a)  

Tags

CCSS.8.EE.C.7B

The mean of the squares of three non-zero numbers a, b, and c is three times the square of their mean. If b=2a, what is the  value of  $\frac{c}{a}$   ?  

Express your answer as a common fraction

(a)  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

A bag contains five red marbles, three blue marbles, and two green marbles. If six marbles are drawn without replacement from the bag, what is the probability that two marbles of each color are drawn.

Express your answer as a common fraction.

(a)  

Tags

CCSS.HSS.CP.B.9

CCSS.HSS.CP.B.8

 $5^2\left(5\right)+5^2\left(11\right)+5^2\left(17\right)+5^2\left(78\right)+5^2\left(14\right)=5^x?$  

What is the value of x in the above equation?

(a)  

Tags

CCSS.7.EE.B.3

CCSS.7.EE.B.4

CCSS.7.NS.A.3

How many miles can Scotty ride on a bike, going at the rate of 8 miles per hour, if he must walk back to the starting point at a rate of 3 miles per hour (following the same route he traveled on his bike) and he is to be gone a total of 11 hours?

(a)  

Tags

CCSS.8.EE.C.7B

Stella sells 30 gismos a month at a price of $20 per gismo. She notices that each time she raises the price of a gismo by $4, she sells 2 fewer gismos per month. What is the maximum amount of revenue, in dollars, that Stella can make in a month of selling gismos?

(a)  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

Mr. Kelly is building a 60-ft-long ramp that will be 24 feet high at the highest point. He wants to place a vertical support beam under the ramp with its top 15 feet down the length of the ramp. How long does he need to make the support ramp?

(a)  

Tags

CCSS.8.G.B.8

Point P is on the y-axis and is equidistant from the points (1, 3) and (7, 5). What is the y-coordinate of point P?

(a)  

Tags

CCSS.HSG.GPE.B.6

Marketing analysts are investigating cylindrical packaging for a new beverage called Star Juice. One member of the design team proposed a can that has a diameter of 6 cm and a height of 20 cm. Another suggested a can that is 17 cm tall and has a diameter of 8 cm. What is the ratio of the smaller volume to the larger volume? Express your answer as a common fraction.

(a)  

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3