Ali made 3 different batches of cookies. She made 3 2/10 batches of vanilla cookies and 7 8/12 batches of chocolate cookies. In total, she made 14 1/6 batches of cookies. How many batches of lemon cookies did she make?

3³/₁₀ batches

Step-by-step explanation:

Let L = the batches of lemon cookies. Then,

3²/₁₀ + 7⁸/₁₂ + L = 14¹/₆ Multiply each side by 60

192 + 460 + 60L = 850 Combine like terms

652 + 60L = 850 Subtract 652 from each side

60L = 198 Divide each side by 60

L = ¹⁹⁸/₆₀ Convert to mixed fraction

L = 3¹⁸/₆₀ Reduce to lowest terms

L = 3³/₁₀

Ali made 3³/₁₀ batches of lemon cookies.

Check:

3²/₁₀ + 7⁸/₁₂ + 3³/₁₀ = 14¹/₆

32/10 + 92/12 + 33/10 = 85/6

192/60 + 460/60 + 198/60 = 850/60

850/60 = 850/60

She made 3 3/10 of lemon cookies.