Solve the problem and answer the question.
-A grocery store has a display of cans in the shape of a trapezoid as shown. There are a total of 30 cans in the display. If the sum of the number of cans in the top row and the bottom row is times the number of cans in
The height of the display, determine the total number of cans in the top and bottom rows.
A) 12 cans
B) 5 cans
C) 60 cans
D) 25 cans

Question

Solve the problem and answer the question.
-A grocery store has a display of cans in the shape of a trapezoid as shown. There are a total of 30 cans in the display. If the sum of the number of cans in the top row and the bottom row is  times the number of cans in
The height of the display, determine the total number of cans in the top and bottom rows. 
A) 12 cans 
B) 5 cans 
C) 60 cans 
D) 25 cans

Quizplus · Accepted Answer

Let the number of cans in the top row be x and the number of cans in the bottom row be y. Then, we can set up the following equations:
x + y = ?  (unknown)
x + y = 11ebb63d_1b60_a1a6_b851_a51d9216278e_TB8475_11h
y - x = h

We can solve for x and y by adding the two equations and dividing by 2 to get y = h + ?/2 and then using the second equation to solve for x:
x = y - h

Substituting these expressions for x and y into the equation 11ebb63d_1b60_a1a6_b851_a51d9216278e_TB8475_11d = x + y, we get:

11ebb63d_1b60_a1a6_b851_a51d9216278e_TB8475_11d = 2y - h

Since we know that the total number of cans is 30 and that the trapezoid has height h, we can set up another equation:

h(11ebb63d_1b60_a1a6_b851_a51d9216278e_TB8475_11d + 2y) = 60

Substituting in the expression for 11ebb63d_1b60_a1a6_b851_a51d9216278e_TB8475_11d, we get:

h(y + y + h) = 60

Simplifying and solving for y, we get:

y = (-h + sqrt(h^2 + 240))/2

Since y is an integer and there are only four answer choices, we can test each choice for h to see which one gives an integer value for y. We find that h = 3 gives y = 8 and x = 7, so the total number of cans in the top and bottom rows is 7 + 8 = 15, which is closest to answer choice A) 12 cans.

Solve the Problem and Answer the Question