Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In a bag full of small balls, 14\frac{1}{4} of these balls are green, 18\frac{1}{8} are blue, 112\frac{1}{12} are yellow and the remaining 2626 white. How many balls are blue?

Full solution

Q. In a bag full of small balls, 14\frac{1}{4} of these balls are green, 18\frac{1}{8} are blue, 112\frac{1}{12} are yellow and the remaining 2626 white. How many balls are blue?
  1. Calculate total number of balls: Calculate the total number of balls in the bag by considering the fractions of green, blue, and yellow balls, and the known quantity of white balls.\newlineLet the total number of balls be TT.\newlineWe know that 14\frac{1}{4} are green, 18\frac{1}{8} are blue, 112\frac{1}{12} are yellow, and the remaining 2626 are white.\newlineSo, (14)T+(18)T+(112)T+26=T\left(\frac{1}{4}\right)T + \left(\frac{1}{8}\right)T + \left(\frac{1}{12}\right)T + 26 = T
  2. Find common denominator: Find a common denominator for the fractions to combine them.\newlineThe common denominator for 44, 88, and 1212 is 2424.\newlineSo, (624)T+(324)T+(224)T+26=T(\frac{6}{24})T + (\frac{3}{24})T + (\frac{2}{24})T + 26 = T\newlineCombine the fractions: (624+324+224)T+26=T(\frac{6}{24} + \frac{3}{24} + \frac{2}{24})T + 26 = T\newline(1124)T+26=T(\frac{11}{24})T + 26 = T
  3. Isolate term with T: Isolate the term with T on one side to solve for T.\newline(1124)T+26=T(\frac{11}{24})T + 26 = T\newlineSubtract (1124)T(\frac{11}{24})T from both sides to get:\newline26=T(1124)T26 = T - (\frac{11}{24})T\newline26=(2424)T(1124)T26 = (\frac{24}{24})T - (\frac{11}{24})T\newline26=(1324)T26 = (\frac{13}{24})T
  4. Solve for T: Solve for T by multiplying both sides by the reciprocal of (1324)(\frac{13}{24}).\newlineT=26×(2413)T = 26 \times (\frac{24}{13})\newlineT=2×24T = 2 \times 24\newlineT=48T = 48\newlineSo, there are 4848 balls in total.
  5. Calculate number of blue balls: Now that we know the total number of balls, calculate the number of blue balls.\newline(1/8)(1/8) of 4848 is the number of blue balls.\newline(1/8)×48=6(1/8) \times 48 = 6

More problems from Add, subtract, multiply, or divide two fractions: word problems

QuestionGet tutor helpright-arrow

Posted 8 months ago