11 x and y are integers such that
3 < x < 8
4 < y < 10
and x + y = 14
Find all the possible values of x. - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 3
Question 11
11 x and y are integers such that
3 < x < 8
4 < y < 10
and x + y = 14
Find all the possible values of x.
Worked Solution & Example Answer:11 x and y are integers such that
3 < x < 8
4 < y < 10
and x + y = 14
Find all the possible values of x. - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 3
Step 1
Find the range for x
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the inequality, we have:
3<x<8
Thus, the possible integer values for x are 4, 5, 6, and 7.
Step 2
Find the range for y
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the inequality, we have:
4<y<10
Thus, the possible integer values for y are 5, 6, 7, 8, and 9.
Step 3
Use the equation x + y = 14
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
We can rearrange the equation to find y:
y=14−x
We will substitute the possible values of x to find valid values for y:
Step 4
Calculate possible values
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Now, substituting the values of x:
If x = 4, then y = 14 - 4 = 10 (not valid)
If x = 5, then y = 14 - 5 = 9 (valid)
If x = 6, then y = 14 - 6 = 8 (valid)
If x = 7, then y = 14 - 7 = 7 (valid)
Thus, the possible values of x which satisfy both conditions are 5, 6, and 7.
