Mdm Tan sold 2/7 of the muffins she baked and Mdm Ong sold 1/2 of he muffins she baked. They had an equal number of muffins left. If Mdm ong baked 120 more muffins than Mdm Tan, how many muffins did Mdm Tan baked?

Madam Tan baked 280 muffins.

Step-by-step explanation:

Madam Tan made x muffins.

She sold 2/7 of the muffins.

That means she kept 5/7 x.

Madam Ong made y muffins.

She sold 1/2 y and kept 1/2 y.

They had an equal number of muffins left.

That gives us 1 equation.

(5/7)x = (1/2)y

Madam Ong baked 120 more muffins than Madam Tan. This gives us a second equation.

y = x + 120

Now we have a system of 2 equations in 2 unknowns.

(5/7)x = (1/2)y

y = x + 120

The second equation is already solved for y, so we can use the substitution method.

(5/7)x = (1/2)(x + 120)

Multiply both sides by 14, the LCD of 7 and 2.

14 * (5/7)x = 14 * (1/2)(x + 120)

2 * 5x = 7(x + 120)

10x = 7x + 840

3x = 840

x = 280

Madam Tan baked 280 muffins.

Check: Since Madam Ong baked 120 more than Madam Tan, 280 + 120 = 400. Madam Ong baked 400 muffins.

Madam Tan sold 2/7 of 280 = 2/7 * 280 = 80. She kept 280 - 80 = 200.

Madam Ong baked 400. She sold half and kept half. She kept 1/2 * 400 = 200. The both kept 200, the same number. Our answer is correct.