Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 12

GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 12

04:43

Video Transcript

Complete the two-way table.

The table has been designed to split 40 students in terms of their hair color and their sex. For example, the five shows that there were five girls with blonde hair. In a similar way, there were six boys with brown hair. The four tells us there were a total of four students boys and girls with ginger hair. The 21 tells us there were a total of 21 girls.

We need to fill in all the missing numbers. At the end, all the numbers inside the paint box will have a sum or total of 40. There are few places we could start this question. But we’ll begin by working out the number of girls with ginger hair. As there are four students in total with ginger hair and there is one boy with ginger hair, we need to subtract one from four. Four minus one is equal to three. Therefore, there are three girls with ginger hair.

Next, we’ll work out the number of boys with black hair. There were 14 students with black hair altogether, six of whom were girls. Therefore, we need to subtract six from 14. 14 minus six is equal to eight. Therefore, there were eight boys with black hair.

Our next step is to work out the total number of boys. There were 40 students in total, 21 of whom were girls. Therefore, we need to subtract 21 from 40. 40 minus 21 is equal to 19. Therefore, there were 19 boys.

Next, we’ll work out the number of boys with blonde hair. There was one boy with ginger hair, six boys with brown hair, eight boys with black hair, and a total of 19 boys. This means that the number of boys with blonde hair plus one plus six plus eight must equal 19. Adding one, six, and eight gives us 15. Therefore, the number of boys with blonde hair plus 15 must equal 19. Subtracting 15 from both sides of this equation gives us an answer of four as 19 minus 15 equals four. Therefore, there are four boys with blonde hair.

We can check this by adding the boys. There were four with blonde hair, one with ginger hair, six with brown hair, and eight with black hair. Four plus one plus six plus eight equals 19.

We can use a similar method to calculate the number of girls that had brown hair. There were five girls with blonde hair, three with ginger hair, six with black hair, and a total of 21 girls. We can write this as an equation: five plus three plus something plus six is equal to 21.

Adding five, three, and six gives us 14. Therefore, 14 plus something equals 21. Subtracting 14 from both sides of this equation gives us an answer of seven as 21 minus 14 is equal to seven. This means there are seven girls with brown hair. Once again, we can check this by adding five, three, seven, and six and getting an answer of 21.

Our final steps are to work out the total number of students that have blonde hair and those that have brown hair. There were four boys with blonde hair and five girls with blonde hair. Therefore, there are a total of nine students with blonde hair. Four plus five equals nine.

In the same way, there were six boys with brown hair and seven girls with brown hair. This gives us a total of 13 students with brown hair as six plus seven equals 13. At this stage, it is worth adding the eight numbers inside the pink box to ensure that they have a total of 14.

Once we’ve checked that all the rows and columns are correct, we can say that we’ve completed the two-way table.

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