Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?

Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 of the remaining in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?

Given:

Mrs Klein sold [tex]\frac{3}{5}[/tex] of the buns in the morning.

Mrs Klein sold [tex]\frac{1}{4}[/tex] of the remaining buns in the evening.

She sold 200 more buns in the morning than afternoon.

To find the total number of buns she make.

Solution:

Let the total number of buns be = [tex]x[/tex]

Number of buns sold in the morning will be given as = [tex]\frac{3}{5}x[/tex]

Number of buns remaining = [tex]x-\frac{3}{5}x[/tex]

Number of buns sold in the evening will be given as = [tex]\frac{1}{4}(x-\frac{3}{5}x)[/tex]

Difference between the number of buns sold in morning and evening = 200

Thus, the equation to find [tex]x[/tex] can be given as:

[tex]\frac{3}{5}x-\frac{1}{4}(x-\frac{3}{5}x)=200[/tex]

Using distribution:

[tex]\frac{3}{5}x-\frac{1}{4}x+(\frac{1}{4}.\frac{3}{5}x)=200[/tex]

[tex]\frac{3}{5}x-\frac{1}{4}x+\frac{3}{20}x=200[/tex]

Multiplying each term with the least common multiple of the denominators to remove fractions.

The L.C.M. of 4, 5 and 20 = 20.

Multiplying each term with 20.

[tex]20\times \frac{3}{5}x-20\times\frac{1}{4}x+20\times\frac{3}{20}x=20\times 200[/tex]

[tex]12x-5x+3x=4000[/tex]

[tex]10x=400[/tex]

Dividing both sides by 10.

[tex]\frac{10x}{10}=\frac{4000}{10}[/tex]

∴ [tex]x=400[/tex]

Thus, total number of buns Mrs Klein made = 400