There were 2/9 as many cakes as buns at a bakery. After selling 1/3 of the buns, there were 68 more buns than cakes left.
(a) How many cakes were there at the bakery at first?
(b) At the end of the day, the baker sold all the cakes at $26 each
How much did he collect from selling all the cakes?
Let's start by using algebra to represent the given information.
Let x be the original number of buns.
Then, the number of cakes is 2/9 of x, which can be written as (2/9)x.
After selling 1/3 of the buns, there were 2/3 of the original number of buns left, which is (2/3)x.
Also, there were 68 more buns than cakes left, which can be written as:
(2/3)x - (2/9)x = 68
Simplifying this equation, we get:
(4/9)x = 68
Multiplying both sides by 9/4, we get:
x = 153
(a) So there were 153 buns at the bakery at first.
The number of cakes is 2/9 of x, which is:
(2/9) x 153 = 34
So there were 34 cakes at the bakery at first.
(b) The baker sold all the cakes at $26 each, so the total amount collected is:
34 x $26 = $884
Let's solve this step-by-step:
(a) Let's assume the number of buns at the bakery is B.
According to the given information, there were 2/9 as many cakes as buns. So, the number of cakes would be (2/9) * B.
After selling 1/3 of the buns, there were 68 more buns than cakes left. After selling 1/3 of the buns, the number of buns remaining would be (2/3) * B. The number of cakes remaining would be (2/9) * B.
According to the given information, the number of buns remaining is 68 more than the number of cakes remaining, so we can create the following equation:
(2/3) * B - (2/9) * B = 68
To solve for B, we need to simplify and solve this equation:
(6/9) * B - (2/9) * B = 68
(4/9) * B = 68
B = (68 * 9) / 4
B = 153
Therefore, there were 153 buns at the bakery at first.
To find the number of cakes, we can substitute the value of B into the equation:
Number of cakes = (2/9) * 153
Number of cakes = 34
So, there were 34 cakes at the bakery at first.
(b) The baker sold all the cakes at $26 each.
To calculate the total amount collected from selling all the cakes, we multiply the number of cakes by the price of each cake:
Total amount collected = Number of cakes * Price per cake
Total amount collected = 34 * $26
Total amount collected = $<<34*26=884>>884
Therefore, the baker collected $884 from selling all the cakes.