How many muffins did maggie sell?

Question

Maggie baked some muffins. 2/3 were bran muffins and the rest were cranberry. She sold 120 cranberry muffins and 7/8 of her bran muffins. Maggie now has 1/6 of her muffins left. How many muffins did she sell?

Answer 1

Let t = total muffins baked

Let s = total muffins sold

let b = bran muffins baked

let c = cranberry muffins baked

 

Translate words to formulas

b = (2/3)t

c = (1/3)t

s = 120 + (7/8)b

t = s + (1/6)t

 

simplify t

t - t/6 = s

5t/6 = s

 

substitute into s equation

5t/6 = 120 + 7b/8

substitute into b formula

5t/6 = 120 + (7/8)*(2/3)*t

Collect terms

t*(5/6 - (7/8)*(2/3) ) = 120

put over common denominator

t*(20/24 - 14/24) = 120

t*6/24 = 120

t/4 = 120

t = 480

substitute to find other values

b = (2/3)*480 = 320

s = 120 + (7/8)*320

s = 120 + 280

s = 400

 

(Didn’t need to know c, it turns out)