Question

For this question, you will need a parent/guardian or a friend. Have this individual grab a handful of coins making sure there are only two types of coins in the group (i.e., nickels and dimes, quarters and pennies, pennies and dimes, etc). Your parent/guardian or friend should tell you the type of coins they’ve chosen, how many coins they have and the dollar amount of the group. From this information, you will set up two sets of equations and determine how many of each coin they have in their hand. Please send your instructor the name of the individual who helped you with this question, your your two equations and the work you did to solve the system.

Answer 1

@Rexy705 can u help?

Answer 2

you want me to make something up?

Answer 3

i have 9 coins only dimes and quarters
the total amount of money is $1.65
how many of each do i have?

Answer 4

idk i need help
@satellite73

Answer 5

lol @question it implies that those whose parent/guardian is no longer alive can't do the question. How terribly restricting..

Answer 6

ok well there is the first part
i came up with a fictitious amount of dimes and quarters and a total amount of money
now comes the second part, you have to figure out how many of each i have

Answer 7

lol @genius12 i guess i am a parent for a day

Answer 8

ok how?

Answer 9

lets put \(x\) as the number of dimes, \(y\) as the total number of quarters, and solve for \(x\) and \(y\)

Answer 10

i told you i had 9 coins all together
how can we write that as an equation with \(x\) and \(y\) ?

Answer 11

x+y=9?

Answer 12

got it! first equation is done

Answer 13

now for the second one
each dime is worth 10 cents, so if i have \(x\) dimes, how much money do i have in dimes
(hint, if i had 13 dimes i would have 130 cents)

Answer 14

if it is not clear, let me know and i will tell you

Answer 15

90?

Answer 16

if i had 9 dimes i would have 90 cents, yes, but i don't have 9 dimes, i have \(x\) dimes
your answer has to have an \(x\) in it

Answer 17

what did you do to 9 to get 90?

Answer 18

like i said, if it is not clear, let me know and i will tell you

Answer 19

did i lose you?

Answer 20

no

Answer 21

it is clear

Answer 22

ok so is it more or less clear that the amount of money i have in times is \(10x\) ?

Answer 23

am i wrong?

Answer 24

if i have 3 dimes i have 30 cents
if i have 6 dimes i have 60 cents
if i have 9 dimes i have 90 cents
if i have \(x\) dimes i have \(10x\) cents

Answer 25

ohhhhh okay

Answer 26

similarly if i have 2 quarters i have 50 cents
if i have 4 quarters i have 100 cents
if i have 7 quarters i have 175 cents

Answer 27

how much if i have \(y\) quarters?

Answer 28

10y?

Answer 29

not quite
\(10\) is for the dime
how many pennies in a quarter?

Answer 30

25

Answer 31

25y?

Answer 32

right

Answer 33

so now the total amount of money: \(10x\) for the dimes, \(25y\) for the quarters, so the total is
\[10x+25y\] which we know is \(165\) so we can say
\[10x+25y=165\]

Answer 34

now we have two equations
\[x+y=9\\10x+25y=165\] and we can solve this for \(x\)

Answer 35

can you help me solve?

Answer 36

any idea how to do it? ("no" is a find answer, i will show you if you do not)

Answer 37

ok i take that as a no

Answer 38

the first equation \(x+y=9\) is the same as saying \(y=9-x\)

Answer 39

then we can replace the \(y\) in the second equation \(10x+25y=165\) by
\(\color{red}{9-x}\) and solve for \(x\)

\[10x+25\color{red}y=165\\
10x+25(\color{red}{9-x})=165\]

Answer 40

multiply out on the left to get
\[10x+225-25x=165\]

Answer 41

collect like terms on the left to get
\[-15x+225=165\]

Answer 42

subtract \(225\) from both sides and get
\[-15x=165-225=-60\] and finally divide both sides by \(-15\) and get
\[x=(-60)\div( -15)=4\]

Answer 43

so i have \(4\) dimes
now the total was \(9\) so how many quarters do i have?

Answer 44

ummm 4?

Answer 45

total is 9
4 dimes
how many quarters?

Answer 46

idk

Answer 47

i don't believe you

Answer 48

i"m confused

Answer 49

9 coins, 4 dimes, how many quarters

Answer 50

5?

Answer 51

yes

Answer 52

because \(9=4+5\)

Answer 53

now lets check the answer
5 quarters and 4 dimes is 9 coins
the 5 quarters are worth $1.25 and the 4 dimes are worth $.40 for a total of
$1.25+.40=1.65

Answer 54

oh thanks that helped a lot

Answer 55

yw

Answer 56

where is says
Please send your instructor the name of the individual who helped you with this question
you can put "satellite73"

Answer 57

lol sure