Q:

In a 4-digit number, the first two digits are both 2. The sum of the ones and tens digits is14. What numbera are possible.

Accepted Solution

A:
Answer:2295, 2286, 2277, 2268, 2259Step-by-step explanation:We are dealing with a number of 4 digits, whose first two digits are 2's. So the number looks like [tex]2~2~ d_2 ~d_1[/tex] (where the last 2 digits are to be determined).The exercise says that the sum of the ones and tens digits is 14. The ones digit is the last digit (the right most digit, which we are denoting by [tex]d_1[/tex]), and the tens digit is the second right most digit (which we are denoting by [tex] d_2[/tex]). So [tex] d_1+d_2=14[/tex]Since they're digits, their only possible values are 0,1,2,3,4,5,6,7,8,9.If d1 was 0, d2 would have to be 14 (since they should add up to 14), which is impossible.If d1 was 1, d2 would have to be 13 (since they should add up to 14), which is impossible.If d1 was 2, d2 would have to be 12, which is impossible.And so going through all possibilities, we get that the only possible ones are:[tex] d1=5~ and~ d_2=9[/tex][tex] d1=6~ and~ d_2=8[/tex][tex] d1=7~ and~ d_2=7[/tex][tex] d1=8~ and~ d_2=6[/tex][tex] d1=9~ and~ d_2=5[/tex]And so the possible 4-digits numbers are 2295, 2286, 2277, 2268, 2259.