Question 643580
Veronica has pennies, nickels, and dimes in her purse, for a total of 32 coins.
 If the number of pennies is 3 more than twice the number of nickels, and the
 number of dimes is 4 less then the number of pennies, 
 how many of each does she have?
:
let p = no. of pennies
let n = no. of nickels
let d = no. of dimes 
:
Write an equation for each statement;
Re-arrange the last two equations get d and n in terms of p:
:
"Veronica has pennies, nickels, & dimes in her purse, for a total of 32 coins."
p + n + d = 32
:
"the number of pennies is 3 more than twice the number of nickels,"
p = 2n + 3
p - 3 = 2n
or 
2n = p - 3
divide both sides by 2
n = {{{((p-3))/2}}}
:
"The number of dimes is 4 less then the number of pennies,"
d = p - 4
:
Replace n and d in the 1st equation
p + {{{((p-3))/2}}} + (p-4) = 32
2p + {{{((p-3))/2}}} = 32 + 4
2p + {{{((p-3))/2}}} = 36
Multiply by 2 to get rid of the fraction
2(2P) + (p-3) = 2(36)
4p + p = 72 + 3
5p = 75
p = 75/5
p = 15 pennies
:
Find the nickels
n = {{{((15-3))/2}}}
n = 6 nickels
:
find dimes
d = 15 - 4
d = 11 dimes
:
:
See if this adds up: 15 + 6 + 11 = 32