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# Help pls

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Patrick bought some dictionaries and files for $1 474. The number of dictionaries he bought was 2/3 the number of files he bought. The cost of a dictionary was$12 more than the cost of a file.

He spent $22 more on dictionaries than on files. How much did a dictionary cost? Aug 26, 2021 ### 4+0 Answers #1 +2 See the following: You now hve four independent equations in four unknowns. Can you take it from here? Sep 3, 2021 #3 0 Sorry Alan, I was working on it at the same time as you. Melody Sep 3, 2021 #2 +1 Patrick bought some dictionaries and files for$1 474.

The number of dictionaries he bought was 2/3 the number of files he bought.

The cost of a dictionary was $12 more than the cost of a file. He spent$22 more on dictionaries than on files.

How much did a dictionary cost?     [Find n]

d dictionaries are bought for n  dollars each    So they will cost a total of   nd dollars

f files are bought for  m dollars   each                so they will cost a total of    mf   dollars

dn + fm = 1474

d= (2/3)f      and   n=m+12

substituting gives us

$$\frac{2}{3}*f (m+12)+fm=1474\\ \frac{2f}{3}*(m+12)+\frac{3fm}{3}=1474\\ 5fm+24f=1474*3\\ f(5m+24)=1474*3\qquad (1)$$

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$$dn=fm+22\\ \frac{2f}{3}(m+12)=fm+22\\ 2fm+24f=3fm+66\\ 24f-fm=66\\ f(24-m)=66\qquad (2)$$

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(1) divided by (2)

$$\frac{f(5m+24)}{f(24-m)}=\frac{3*1474}{66}\\ \frac{(5m+24)}{(24-m)}=67\\ 5m+24=67*24-67m\\ 72m=66*24\\ m=22\\~\\ n=22+12=34$$

the dictionaries cost   \$34 each

Sep 3, 2021