A bakery baked buns and cakes in the morning in the ratio 4:1
After selling 50 buns and 10 cakes in the afternoon, the ratio of the number of buns to the number of cakes left became 3:1
a) Find the number of bums that the bakery baked in the morning
b) Find the number of cakes left
Please help, thanks
original buns ---- 4x
original cakes --- x
after sale:
buns ---- 4x-50
cakes ---- x-10
(4x-50)/(x-10) = 3/1
4x - 50 = 3x - 30
take over
To solve this problem, we can use the concept of ratios and proportions. Let's break it down step by step:
a) To find the number of buns that the bakery baked in the morning, let's assume that they baked 4x buns and x cakes.
After selling 50 buns and 10 cakes in the afternoon, the number of buns left would be 4x - 50, and the number of cakes left would be x - 10.
According to the given information, the ratio of the number of buns to the number of cakes left became 3:1 after the sales. This can be expressed as:
(4x - 50) / (x - 10) = 3/1
To solve this equation, we can cross-multiply:
3(x - 10) = 4x - 50
3x - 30 = 4x - 50
Subtract 3x from both sides:
-30 = x - 50
Add 50 to both sides:
20 = x
Therefore, the number of cakes baked in the morning was 20.
To find the number of buns:
4x = 4 * 20 = 80
Hence, the bakery baked 80 buns in the morning.
b) Now that we have the number of cakes left (20), we can find the number of buns left.
The number of buns left is 4x - 50:
4 * 20 - 50 = 80 - 50 = 30
Therefore, the number of cakes left is 20, and the number of buns left is 30.
I hope this explanation helps! Let me know if you have any further questions.