+176 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?
+33661 See the following:
You now hve four independent equations in four unknowns. Can you take it from here?
+118667 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
