3/7 of the muffins in the bakery were carrot muffins. The number of blueberry muffins was twice the number of multi grain muffins. The number of multi-grain muffings was 1/3 the number of banana muffins. If there were 108 multi0grain muffins, how many carrot muffins were there?
multigrain -- 108
banana ----- 324
blueberry --- 216
carrot ------- x
(3/7)(total) = x
(3/7)( 108+324+216+x) = x
3(648+x) = 7x
1944 + 3x = 7x
4x = 1944
x = 486
There were 486 carrot muffins
check:
total = 108+324+216+486 = 1134
is (3/7)(1134) = 486 ?? YES
To find the number of carrot muffins, we need to determine the total number of muffins in the bakery.
We know that 108 multi-grain muffins were there, which is 1/3 of the number of banana muffins.
So, the number of banana muffins is 108 x 3 = 324.
The number of blueberry muffins is twice the number of multi-grain muffins, which is 2 x 108 = 216.
The total number of muffins in the bakery is the sum of carrot, multi-grain, blueberry, and banana muffins,
which is: carrot + multi-grain + blueberry + banana = carrot + 108 + 216 + 324.
It is given that 3/7 of the muffins in the bakery were carrot muffins. So, 3/7 = carrot / (carrot + 108 + 216 + 324).
To solve for the number of carrot muffins, we can cross-multiply:
3(carrot + 108 + 216 + 324) = 7 (carrot).
We can distribute and simplify this equation:
3carrot + 324 + 648 + 972 = 7carrot.
Combine like terms:
1944 = 4carrot.
Divide both sides of the equation by 4:
1944 / 4 = carrot.
The number of carrot muffins is 486.
To find the number of carrot muffins, we need to follow the given information step-by-step.
1. Let's start with the number of multi-grain muffins. According to the information, there were 108 multi-grain muffins.
2. It is stated that the number of multi-grain muffins was 1/3 the number of banana muffins. Therefore, we can calculate the number of banana muffins by multiplying the number of multi-grain muffins (108) by 3: 108 * 3 = 324 banana muffins.
3. The number of blueberry muffins was twice the number of multi-grain muffins. So, we can calculate the number of blueberry muffins by multiplying the number of multi-grain muffins (108) by 2: 108 * 2 = 216 blueberry muffins.
4. Lastly, we know that 3/7 of the muffins in the bakery were carrot muffins. To find the number of carrot muffins, we need to subtract the total number of multi-grain, banana, and blueberry muffins from the total number of muffins.
Let's calculate the total number of muffins: multi-grain muffins (108) + banana muffins (324) + blueberry muffins (216) = 648.
To find 3/7 of 648, we multiply it by 3/7: 648 * (3/7) = 648/7 * 3 = 216 carrot muffins.
Therefore, there were 216 carrot muffins in the bakery.