SOLUTION: This is a system of equation problem and I am not sure what I need to do as we are just starting them. Could you please help me out? The question is How many days before 17th Augu

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Question 548227: This is a system of equation problem and I am not sure what I need to do as we are just starting them. Could you please help me out? The question is How many days before 17th August is it, if 50 days ago it was four times as many since March 30th?
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of days before August 17
-------------------------------------
given:
days before August 17 it was
days since March 30
-------------------------
= number of days between
March 30 and August 17
---------------------
March 31 = 1 day
April has 30 days
May has 31
June has 30
July has 31
There are 16 days before August 17




I'll call it 18 days
check:
August 17 minus 18 days is July 31
July 31 minus 50 days is June 10
---------------------------

Is it 72 days since March 30?
days
---------------------------
I believe 18 days is the answer, but I lost
1 day somehow in my calculations
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
The other tutor made an error, noticed it and quit, which tutors
should not do.

The problem is:

How many days before August 17 is "today", if 50 days ago "today"
it was four times that many days since March 30th? 
You need a date number list like the one below.  This one is for a 
non-leap year, but you can put in Feb. 29, like we will have in 2012
if you like.  It will just make the date numbers come out one less.
But the answer will be the same, since, luckily, all the dates are
after February.

 1. January 1
 2. January 2
 3. January 3
 4. January 4
 5. January 5
 6. January 6
 7. January 7
 8. January 8
 9. January 9
10. January 10
11. January 11
12. January 12
13. January 13
14. January 14
15. January 15
16. January 16
17. January 17
18. January 18
19. January 19
20. January 20
21. January 21
22. January 22
23. January 23
24. January 24
25. January 25
26. January 26
27. January 27
28. January 28
29. January 29
30. January 30
31. January 31
32. February 1
33. February 2
34. February 3
35. February 4
36. February 5
37. February 6
38. February 7
39. February 8
40. February 9
41. February 10
42. February 11
43. February 12
44. February 13
45. February 14
46. February 15
47. February 16
48. February 17
49. February 18
50. February 19
51. February 20
52. February 21
53. February 22
54. February 23
55. February 24
56. February 25
57. February 26
58. February 27
59. February 28
60. March 1
61. March 2
62. March 3
63. March 4
64. March 5
65. March 6
66. March 7
67. March 8
68. March 9
69. March 10
70. March 11
71. March 12
72. March 13
73. March 14
74. March 15
75. March 16
76. March 17
77. March 18
78. March 19
79. March 20
80. March 21
81. March 22
82. March 23
83. March 24
84. March 25
85. March 26
86. March 27
87. March 28
88. March 29
89. March 30
90. March 31
91. April 1
92. April 2
93. April 3
94. April 4
95. April 5
96. April 6
97. April 7
98. April 8
99. April 9
100. April 10
101. April 11
102. April 12
103. April 13
104. April 14
105. April 15
106. April 16
107. April 17
108. April 18
109. April 19
110. April 20
111. April 21
112. April 22
113. April 23
114. April 24
115. April 25
116. April 26
117. April 27
118. April 28
119. April 29
120. April 30
121. May 1
122. May 2
123. May 3
124. May 4
125. May 5
126. May 6
127. May 7
128. May 8
129. May 9
130. May 10
131. May 11
132. May 12
133. May 13
134. May 14
135. May 15
136. May 16
137. May 17
138. May 18
139. May 19
140. May 20
141. May 21
142. May 22
143. May 23
144. May 24
145. May 25
146. May 26
147. May 27
148. May 28
149. May 29
150. May 30
151. May 31
152. June 1
153. June 2
154. June 3
155. June 4
156. June 5
157. June 6
158. June 7
159. June 8
160. June 9
161. June 10
162. June 11
163. June 12
164. June 13
165. June 14
166. June 15
167. June 16
168. June 17
169. June 18
170. June 19
171. June 20
172. June 21
173. June 22
174. June 23
175. June 24
176. June 25
177. June 26
178. June 27
179. June 28
180. June 29
181. June 30
182. July 1
183. July 2
184. July 3
185. July 4
186. July 5
187. July 6
188. July 7
189. July 8
190. July 9
191. July 10
192. July 11
193. July 12
194. July 13
195. July 14
196. July 15
197. July 16
198. July 17
199. July 18
200. July 19
201. July 20
202. July 21
203. July 22
204. July 23
205. July 24
206. July 25
207. July 26
208. July 27
209. July 28
210. July 29
211. July 30
212. July 31
213. August 1
214. August 2
215. August 3
216. August 4
217. August 5
218. August 6
219. August 7
220. August 8
221. August 9
222. August 10
223. August 11
224. August 12
225. August 13
226. August 14
227. August 15
228. August 16
229. August 17
230. August 18
231. August 19
232. August 20
233. August 21
234. August 22
235. August 23
236. August 24
237. August 25
238. August 26
239. August 27
240. August 28
241. August 29
242. August 30
243. August 31
244. September 1
245. September 2
246. September 3
247. September 4
248. September 5
249. September 6
250. September 7
251. September 8
252. September 9
253. September 10
254. September 11
255. September 12
256. September 13
257. September 14
258. September 15
259. September 16
260. September 17
261. September 18
262. September 19
263. September 20
264. September 21
265. September 22
266. September 23
267. September 24
268. September 25
269. September 26
270. September 27
271. September 28
272. September 29
273. September 30
274. October 1
275. October 2
276. October 3
277. October 4
278. October 5
279. October 6
280. October 7
281. October 8
282. October 9
283. October 10
284. October 11
285. October 12
286. October 13
287. October 14
288. October 15
289. October 16
290. October 17
291. October 18
292. October 19
293. October 20
294. October 21
295. October 22
296. October 23
297. October 24
298. October 25
299. October 26
300. October 27
301. October 28
302. October 29
303. October 30
304. October 31
305. November 1
306. November 2
307. November 3
308. November 4
309. November 5
310. November 6
311. November 7
312. November 8
313. November 9
314. November 10
315. November 11
316. November 12
317. November 13
318. November 14
319. November 15
320. November 16
321. November 17
322. November 18
323. November 19
324. November 20
325. November 21
326. November 22
327. November 23
328. November 24
329. November 25
330. November 26
331. November 27
332. November 28
333. November 29
334. November 30
335. December 1
336. December 2
337. December 3
338. December 4
339. December 5
340. December 6
341. December 7
342. December 8
343. December 9
344. December 10
345. December 11
346. December 12
347. December 13
348. December 14
349. December 15
350. December 16
351. December 17
352. December 18
353. December 19
354. December 20
355. December 21
356. December 22
357. December 23
358. December 24
359. December 25
360. December 26
361. December 27
362. December 28
363. December 29
364. December 30
365. December 31

Let's let x = the date number of "today" (or, rather, the date we are
PRETENDING is "today" for this problem) 

Let's let y = the number of days from "today" until August 17th.

We have four dates to consider:

"Today", which is date number x
March 30, which was date number 89.
50 days ago "today", which was date number x-50
August 17, which is date #229

So we have:

(Today) + (y days) = (August 17)

That gives us the first equation:

             x + y = 229  

Which is already simplified. 

We must subtract 4 times as many days from (50 days ago) 
as "today" is before August 17 to get back to March 30.

Therefore  

(50 days ago) - (4 times y days) = (March 30)

That gives us the equation:

       (x-50) - 4y = 89   

Simplifying that

       x - 50 - 4y = 89
            x - 4y = 139

So the system of equations is

            x  + y = 229
            x - 4y = 139

Solve the first equation for x

            x  + y = 229
                 x = 229 - y

Substitute that for x in

            x - 4y = 139
    (229 - y) - 4y = 139
      229 - y - 4y = 139
          229 - 5y = 139
               -5y = -90
                 y = 
                 y = 18

That's actually the answer, but to check it we
must also find x, by substituting 18 for y in

                 x = 229 - y
                 x = 229 - 18
                 x = 211

So "today" is July 30, date #211.
In 18 days from "today", it will be date #211 + 18 = #229,
or August 17.  That checks.

50 days ago from "today" was #211-50 = #161, or June 10.

The number of days March 30 was before June 10 was #161-#89 or 72 days,

It is 18 days from "today", July 30, until August 17, and since
72 days is 4 times 18, then March 30 is 4 times as many days before
June 10 as August 17 is from "today", July 30.

So it checks.

The answer is 18 days.  (If you use leap year date numbers, all the
date numbers will be 1 less, but the answer will still be 18.

Edwin
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