Muffins were sold in three flavors in a bakery. There were 44 more chocolate muffins than vanilla muffins. There were twice as many chocolate muffins as blueberry muffins. All the blueberry muffins were sold. 3/4 of the chocolate muffins and 5/6 of the vanilla muffins were also sold. There were 71 muffins left. How many muffins were sold?
There were 44c than v twice as many blueberry than c 88 b sold. 3/4=0.75 and 5/6=0.833
Try ti work it out from there
number of vanillas --- x
number of chocs = x + 44
"There were twice as many chocolate muffins as blueberry muffins"
--- number of blueberries = 1/2 chocs
= (1/2)(x+44) = x/2 + 22
after sale, 1/4 of the chocs and 1/6 of vanillas are left, which is 71
(1/4)(x+44) + (1/6)x = 71
times 12
3(x+44) + 2x = 852
3x + 132 + 2x = 852
5x = 720
x = 144
so...
vanillas --- 144
chocholates --- 188
blueberries ----94
total muffins = 144+188+94 = 426
left over = 71
muffins sold = 426-71 =355
check:
sold 3/4 of chocs, leaving 47
sold 5/6 of vanillas, leaving 24
total left over = 47+24 = 71
I have the correct answers
To find out how many muffins were sold, we first need to determine the number of chocolate, vanilla, and blueberry muffins.
Let's start by assigning variables to each type of muffin:
Let's call the number of chocolate muffins as C,
the number of vanilla muffins as V,
and the number of blueberry muffins as B.
From the given information, we have the following conditions:
1. There were 44 more chocolate muffins than vanilla muffins:
C = V + 44. (Equation 1)
2. There were twice as many chocolate muffins as blueberry muffins:
C = 2B. (Equation 2)
3. All the blueberry muffins were sold:
B = 0. (Equation 3)
4. 3/4 of the chocolate muffins and 5/6 of the vanilla muffins were sold:
Remaining chocolate muffins = 1 - 3/4 = 1/4 of C.
Remaining vanilla muffins = 1 - 5/6 = 1/6 of V.
5. There were 71 muffins left:
Remaining muffins = Remaining chocolate muffins + Remaining vanilla muffins + Remaining blueberry muffins.
71 = 1/4 C + 1/6 V + 0.
Now we can solve the equations to find the values of C and V.
From equation 1, we substitute C = V + 44 into equation 2:
V + 44 = 2B.
Since all blueberry muffins were sold (equation 3), B = 0.
This means V + 44 = 2 * 0,
which simplifies to V + 44 = 0 or V = -44.
Since the number of muffins cannot be negative, we discard this solution.
Therefore, there must be another condition that satisfies the given information.
Let's reconsider equation 2:
C = 2B.
Since all blueberry muffins were sold (equation 3), B = 0.
This implies C = 2 * 0, so C = 0.
If there are no chocolate muffins (C = 0), then we cannot satisfy the condition mentioned where there were 44 more chocolate muffins than vanilla muffins (C = V + 44).
Therefore, there is not enough information to solve this problem.