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Mary and Joseph baked some muffins each. If Mary gives Joseph 26 muffins, Joseph will have 3/4 as many muffins as Mary. If Joseph gives Mary 30 muffins, Joseph will have 25% as many muffins as Mary. How many muffins did Mary bake?

 Apr 4, 2022
 #1
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(j + 26)  = 3/4 (m-26)

(j-30) = 1/4 ( m+ 30)                solve system of equations to find  j  m 

 Apr 4, 2022
 #2
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(j + 20) = 3/4 (m - 26)

(j - 30) = 1/4 (m + 30)

 

4j + 104 = 3m - 78 - (1)

4j - 120 = m + 30 - (2)

Subs (1) from (2) we get

224 = 2m - 108

2m = 332

m = 166

Putting value of m in eqm (1)

 

(j + 26) = 3/4 (166 - 26)

(j + 26) 3/4 (140)

(j + 26) = 3 * 35

j + 26 = 105

j = 79

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