Digit Problems: Find the NumberDate: 01/29/98 at 19:45:52 From: Kara Subject: Algebra 1 (Digit Problems) My teacher explained digit problems in school. I thought I had gotten it, and so far I have found the right answers to the first three homework problems. I thought I was getting the hang of it until I stumbled upon one I couldn't figure out - and to my dismay the next four were the same. Here they are: 1. A two-digit number is 6 more than 4 times the sum of its digits. The digits from left to right are consecutive even integers. Find the number. 2. A two-digit number is five times the sum of its digits. The digits from left to right name consecutive integers. Find the number. 3. A two digit number is 5 times the sum of its digits. When 9 is added to the number, the result is the original number with its digits reversed. Find the number. Hint: The number with its digits reversed is 10u +t. 4. The sum of the digits of a two digit number is 9. The number is 27 more than the original number with its digits reversed. Find the number. 5. The units digit of a two-digit number is 2 less than the tens digit. The number is two more than 6 times the sum of the digits. Find the number. I am pretty sure I am setting them up right, for example No. 5, the one I understood best: t-u = 2 6(t+u)+2 = 10t+u Numbers 1-4 are the hardest. I would appreciate it if you did one of those and showed me it step by step. Thanks Doc! Date: 02/01/98 at 11:13:54 From: Doctor Wolf Subject: Re: Algebra 1 (Digit Problems) Okay, Kara - Let's get started! You've done a nice job of setting up no. 5, and I'm assuming you can solve it from there. I will do problem no. 1 completely, and set up no. 2 for you. Problem 1: A two-digit number is 6 more than 4 times the sum of its digits. The digits from left to right are consecutive even integers. Find the number. The fact that the digits from left to right are consecutive even integers means that the number must look like 24, or 46, or possibly 68. Moreover, if we let t = the tens digit (as you did in no. 5), then t+2 = the units digit Okay so far? A two-digit number is 6 more than 4 times the sum of its digits can now be written as: 10t + (t+2) = 6 + 4(t + t+2), or 10t + t+2 = 6 + 4(2t + 2), now use the distributive property 10t + t+2 = 6 + 8t + 8, now combine like terms 11t + 2 = 8t + 14, now subtract 8t from both sides of "=" 3t + 2 = 14, now subtract 2 from both sides of "=" 3t = 12, or t = 4 So the tens digit, or t, is 4! This means the units digit must be 6 and the next consecutive even integer, and so our number is 46. Let's check this out. 46 is 6 more than 4 times (4+6), or 46 is 6 more than 40 Yes! I'll get you started on no. 2. A two-digit number is five times the sum of its digits. The digits from left to right name consecutive integers. Find the number. If the digits from left to right name consecutive integers, then the number must look like 12, or 34, or 89, etc. This means if you let t = the tens digit, then t+1 will represent the units digit. Therefore 10t + (t+1) = 5(t + t+1) Take it from there Kara! I hope this helped, and don't hesitate to stop in again. -Doctor Wolf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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