Answer:
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
Answer: 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.
