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Taylor performs in a show - OCR - GCSE Maths - Question 15 - 2023 - Paper 2
Question 15
Taylor performs in a show. Taylor spends 1/8 of the show singing, 1/4 of the show dancing and the remaining 55 minutes backstage. Work out how long the show lasted.... show full transcript
Worked Solution & Example Answer:Taylor performs in a show - OCR - GCSE Maths - Question 15 - 2023 - Paper 2
Step 1
Work out the total fraction of time spent singing and dancing
Answer
Taylor's time spent singing is given as ( \frac{1}{8} ) and dancing as ( \frac{1}{4} ).
We first convert ( \frac{1}{4} ) to eighths:
( \frac{1}{4} = \frac{2}{8} ).
Now we can add the two fractions:
( \frac{1}{8} + \frac{2}{8} = \frac{3}{8} ).
Thus, Taylor spends ( \frac{3}{8} ) of the show either singing or dancing.
Step 2
Calculate the remaining time
Answer
The total time spent singing and dancing is ( \frac{3}{8} ) of the show. The remainder of the time is backstage, which is 55 minutes.
This means the remaining fraction of time is:
( 1 - \frac{3}{8} = \frac{5}{8} ).
Let ( T ) represent the total time of the show in minutes. Therefore, we can set up the equation:
( \frac{5}{8} T = 55 ).
Step 3
Step 4