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.

step-by-step explanation:

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step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

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the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights