# How do I figure out this problem? You have 37 coins (all nickels , dimes, and quarters) adding up to \$5.50. You have 4 more quarters than nickels. How many dimes do you have?

Let q,d and n stand for the number of quarters, dimes and nickels you have respectively. Thus we know
(1) q + d + n = 37
(2) .25q + .10d + .05n = 5.50
(3) q = n + 4

We can use (3) to eliminate q in (1) and (2) to get
(n+4) + d + n= 37 or
(1') 2n +d =33

.25(n+4) + .10d + .05n = 5.50 or,
.25n + 1 +.1d +.05n = 5.50 so
(2').30n +.10d =4.50

From (1') d = 33-2n Use that for d in (2') to solve for n. Let us know if you need further help.

Thanks

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
{"ft_lang_label":"__label__en","ft_lang_prob":0.9679735,"math_prob":0.99951804,"size":5344,"snap":"2022-40-2023-06","text_gpt3_token_len":1672,"char_repetition_ratio":0.19456929,"word_repetition_ratio":0.083798885,"special_character_ratio":0.3261602,"punctuation_ratio":0.127378,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9976143,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T20:30:10Z\",\"WARC-Record-ID\":\"<urn:uuid:ab7c3f2d-21f9-44da-aade-6e8c05618a4c>\",\"Content-Length\":\"20021\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c6d4b948-ff47-4f1f-b545-8914bf624b72>\",\"WARC-Concurrent-To\":\"<urn:uuid:629e96f9-6169-440b-8f1d-8e3545329c10>\",\"WARC-IP-Address\":\"45.79.29.166\",\"WARC-Target-URI\":\"https://questions.llc/questions/1877/how-do-i-figure-out-this-problem-you-have-37-coins-all-nickels-dimes-and-quarters\",\"WARC-Payload-Digest\":\"sha1:DEX4S3MMFG3APFBXSC2QCPIEWSP2SAQN\",\"WARC-Block-Digest\":\"sha1:FRHH3HRMOVFW5M7HGIXQVCHCYJZK7KS7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337432.78_warc_CC-MAIN-20221003200326-20221003230326-00598.warc.gz\"}"}