You know that there are 46 dimes and quarters in a jar. When you count up the money you find you have a total of $9.40. How many dimes are there? How many quarters?

Question

You know that there are 46 dimes and quarters in a jar.  When you count up the money you find you have a total of $9.40.  How many dimes are there?  How many quarters?

amistre64 · Answer

setup a system of equations

d + q = 46

.10d + .25q = 9.40

anonymous · Answer

So do you solve for D or Q? and how

amistre64 · Answer

i would solve for d.imes and q.uarters yes.

and your material should give you at least 3 ways to approach a solution.  use the one you are most comfortable with.

amistre64 · Answer

elimination seems to be the simplest approach to me since the top is practically bare of coeffs ...

but many like subsitution better

amistre64 · Answer

let d = (23+n)  and q=(23-n)

d + q = 46

23 + n + 23 - n = 46 ... by default

substitute them into the second equation and solve for n.

anonymous · Answer

Ummm ok how do you do substitution? I know what substitution is and I know the equation, I just don't know how to use the two together.

anonymous · Answer

Where does 23 come from?

amistre64 · Answer

one type of substitution i just mentioned

the other type is to solve one equation for a term, and replace it in the other equation

if  ax + by = c,  we can solve for a:  a = (c-by)/x

this is one type of relationship that must be satisfied so we simply let all a's be (c-by)/x

amistre64 · Answer

23 is a convenient number

since 23 + 23 = 46  and n-n = 0  its just useful to define them that way

amistre64 · Answer

d = 23 + n
+ q = 23 - n
------------
  46 = 46 + 0

amistre64 · Answer

.10d + .25q = 9.40

substitute for d and q

.10(23+n) + .25(23-n) = 9.40

now we only have one variable to solve

anonymous · Answer

n= -9

amistre64 · Answer

very good

now we know d and q

d = 23 + n = 23 - 9
q = 23 - n = 23 + 9

anonymous · Answer

So what do we do now?

amistre64 · Answer

^^^^ look at the post above ..

anonymous · Answer

d = 23 + n = 23 - 9
q = 23 - n = 23 + 9
doesn't answer the question

amistre64 · Answer

im pretty sure it does ..... what question are we trying to answer?

anonymous · Answer

How many dimes? How many quarters?

amistre64 · Answer

so how many d.imes do we have?

amistre64 · Answer

d = 23 + n,  and n=-9

anonymous · Answer

14?

amistre64 · Answer

yep

how many q.uarters so we have?

q = 23 - n ; and n=-9

amistre64 · Answer

or if you want to use our fundamental equation:  14 + q = 46