how many numbers between 650 and 780 leave remainders of 4 and 6 when divided by 7 and 11 respectively? pls help lol im desperate...
Accepted Solution
A:
Answer:18 numbers between 650 and 780 leave remainders of 4 when divided by 7.12 numbers between 650 and 780 leave remainders of 6 when divided by 11.Step-by-step explanation:1. Number 655 is the smallest number that leaves the remainder of 4 when divided by 7. Number 774 is the greatest number that leaves the remainder of 4 when divided by 7. So,[tex]a_1=655\\ \\a_n=774\\ \\d=7\\ \\a_n=a_1+(n-1)d\Rightarrow 774=655+7(n-1)\\ \\7(n-1)=774-655\\ \\7(n-1)=119\\ \\n-1=17\\ \\n=17+1=18[/tex]2. Number 655 is the smallest number that leaves the remainder of 6 when divided by 11. Number 776 is the greatest number that leaves the remainder of 6 when divided by 11. So,[tex]a_1=655\\ \\a_n=776\\ \\d=11\\ \\a_n=a_1+(n-1)d\Rightarrow 776=655+11(n-1)\\ \\11(n-1)=776-655\\ \\11(n-1)=121\\ \\n-1=11\\ \\n=11+1=12[/tex]