Question 1158500
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No!  DON'T use 4 variables and write and solve a system of 4 equations...!<br>
Take the time to analyze the given information and try to write a single equation.<br>
The first piece of information is "one-third as many halves as dimes".  We could let our variable x be the number of dimes; but then the number of halves would be (1/3)x.  Fractions always make calculations more complicated; so let's start with our variable x as the number of halves.  So<br>
let x = # of half dollars
then 3x = # of dimes  ["one third as many halves as dimes"]
then 6x = # of quarters  ["twice as many quarters as dimes"]
then x+7 = # of dollars  ["7 more dollars than halves"]<br>
Now we have a single equation in one variable to solve -- far less work than solving a system of 4 equations and 4 unknowns.<br>
Writing the equation in cents (again to avoid the difficulty of working with decimals):
{{{50(x)+10(3x)+25(6x)+100(x+7) = 2350}}}
{{{50x+30x+150x+100x+700 = 2350}}}
{{{330x = 1650}}}
{{{x = 1650/330 = 5}}}<br>
ANSWER:
dollars: x+7 = 12
halves: x = 5
quarters: 6x = 30
dimes: 3x = 15<br>
CHECK: {{{12(100)+5(50)+30(25)+15(10) = 1200+250+750+150 = 2350}}}<br>