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Question

A baker is gathering the ingredients required to make 15 batches of oatmeal cookies and 1 cake. The cake will require one-quarter bag of flour. The baker needs a total of more than 3 but less than 4 bags of flour. What is one possible value for the fraction of one bag of flour required for each batch of cookies?

The correct answer is: 0.183 < x < 0.25

HINT :- let the fraction of flour required for 1 batch of cookies be x and flour required for 1 cake is $1 fourth$ . let the total flour required be T where (3 < T < 4) . Now, find T in terms of x and substitute in place of T in the inequality to find the range of values of x.
total flour required T = flour required for 15 batches of cookies + cake
T = 15x + $1 fourth$
3 < T < 4 $not stretchy rightwards double arrow space 3 space less than space 15 straight x space plus space open parentheses fraction numerator begin display style 1 end style over denominator 4 end fraction close parentheses less than space 4 space not stretchy rightwards double arrow space open parentheses fraction numerator begin display style 11 end style over denominator 4 end fraction close parentheses space less than space 15 straight x space less than space open parentheses fraction numerator begin display style 15 end style over denominator 4 end fraction close parentheses$
$not stretchy rightwards double arrow space open parentheses fraction numerator begin display style 11 end style over denominator 60 end fraction close parentheses space less than space straight x space less than space open parentheses fraction numerator begin display style 15 end style over denominator 60 end fraction close parentheses$

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