Answer: Liam has 52 chairs.
Step-by-step explanation:
Let x= Number of chairs in each row.
If he arranges the chairs in 9 rows and 7 chairs left over.
Then total chairs = 9x+7
If he arranges the chairs in 7 rows and 17 left over.
Total chairs = 7x+17
Now, [tex]9x+7=7x+17[/tex]
[tex]\Rightarrow\ 9x-7x=17-7\\\\\Rightarrow\ 2x=10\\\\\Rightarrow\ x=5[/tex]
Total chairs = 9(5)+7 = 45+7= 52
Hence, Liam has 52 chairs.
Answer:
367
Step-by-step explanation:
Let there be x chair in each row of 9 rows.
So, the number of chair in 9 rows = 9x
As 7 chair left-over, so, the number of chair in a row is more than 7, i.e
[tex]x>7\cdots(i)[/tex]
Total numbers of the chair [tex]= 9x+7 ...(ii)[/tex]
Similarly, let there be y chair in each row of 7 rows.
So, the number of chair in 7 rows = 7x
As 17 chair left-over, so, the number of chair in a row is more than 17, i.e
[tex]y>17\cdots(iii)[/tex]
so total numbers of the chair [tex]= 7x+17 ...(iv)[/tex]
From equation (ii) and (iv),
[tex]9x+7=7x+17[/tex]
[tex]\Rightarrow 9x-7y=10\cdots(v)[/tex]
As x and y are the numbers of chairs in a row, so it must be a counting number.
So, to satisfy the equation (iv), the possible values of (x, y) are
[tex](x,y)=(5,5),(12,14), (40,50), (110,140),\cdots[/tex] and so on.
Now, from equations (i) and (iii), the possible values are
(x,y)= (40,50), (110,140), ...
Now, to get the minimum number of chairs, put x=40 in the equation (ii) or put y=50 in the equation (iv),
So, total number of chair=
[tex]9x+7=9\times40 +7 =367.[/tex]
For (x,y)=(110,140)
Total number of chair=
[tex]9x+7=9\times110 +7 =997.[/tex]
Similarly, the other possibility can be determined.
Hence, the total (minimum) number of chair is 367
