Question

Nadya has 36 blueberries and 45 raspberries that she will be putting into cups of yogurt to make after-school snacks. She wants to put an equal number of blueberries and an equal number of raspberries into each cup. She uses all the berries. Use the drop-down menus to complete the statements below about the number of cups Nadya can make.

If Nadya wants to use all the berries and put an equal number of blueberries and raspberries into each cup, she can make the maximum number of cups by putting:
A) 2 blueberries and 2 raspberries in each cup.
B) 3 blueberries and 4 raspberries in each cup.
C) 4 blueberries and 3 raspberries in each cup.
D) 5 blueberries and 5 raspberries in each cup.

Answer 1

The correct answer is 9 blueberries and 9 raspberries per cup, making a total of 4 cups, as 9 is the largest number that divides both 36 and 45 evenly.

Step-by-step explanation:

To determine the number of cups Nadya can make with equal numbers of blueberries and raspberries, we need to look for the largest common divisor that can be applied equally to both 36 blueberries and 45 raspberries. This number will tell us how many of each berry Nadya can place in each cup and thus, how many cups she can make in total.

Upon examining the quantity of blueberries and raspberries, we can deduce that the largest number that evenly divides both 36 and 45 is 9. Therefore, Nadya can put 9 blueberries and 9 raspberries into each cup.

The correct answer is neither A, B, C, nor D, as none of these choices divides both numbers of berries evenly. Instead, the answer would be 9 blueberries and 9 raspberries in each cup. This means she can make 4 cups since 36 divided by 9 equals 4, and 45 divided by 9 equals 5. Since she wants to use all berries equally, she will go with the smaller number of cups.