Question

bob has $2.90 in pennies nickels and dimes. he has the same number of pennies and nickels. if the number of dimes is 5 more than the number of nickels, how many of each type of coin does he have? Step by step explanation?

Answer 1

lets say we have "d" number of dimes and "n" number of nickels
now the question states we have 5 more dimes than nickels
this can be represented as
n+5=d

the dime is worth $.10
the nickel is worth $.05
the total amount of money you have is $2.90

so ".10d" would be the amount of money in dimes
.05n would be the amount of money in nickels

the sum of those two must be equal to 2.90

.10d+.05n=2.90

now you have 2 equations with 2 unknowns
you substitute one equation into the other to solve for the number of nickels or dimes
(in this case nickels first)

then use the number of nickels to solve for the number of dimes

Answer 2

what about pennies?

Answer 3

oh crap there are pennies

Answer 4

yeah

Answer 5

the number of pennies are equal to the number of nickels
p=n
revising
.01p+.05n+.10d=2.90
n+5=d
p=n

3 equations 3 unknowns
just solve by substitution

Answer 6

where does that go?

Answer 7

do you understand what substitution is?

Answer 8

no

Answer 9

if y=n
and we have
x+y=0
substitution is replacing the y with an n because n is equal to y

so x+n=0

another example
if y=x+1

and w+y=5
because y is equal to (x+1), we can "substitute" (x+1) for y

w+(x+1)=5

understand it now?

Answer 10

sorta but can you go through it step by step?

Answer 11

do i have to?????

.01p+.05n+.10d=2.90
n+5=d
p=n

substitute so that the first equation has only 1 variable


.01(n)+.05n+.10(n+5)=2.90

then solve for n

once you determine n, use the original equations to solve for p and d