Question

Last one :P

Mia deposits either $5 or $3.50 into her savings account. She made 14 deposits equaling a total of $59.50.

How many times did she deposit $5 and how many times did she deposit $3.50?

Mia made deposits of $5 and deposits of $3.50.

Answer 1

she made 14 deposits
TOTALing 59.50

so whatever amount was for $5, let's say "x"
so whatever amount was for $3.50, let's say "y"

whatever those amounts are, they both sum up to 14, since it was only 14 deposits
\(\Large \bf x +y =14\)

how much was that in money? well "x" amount at $5 each is 5x
what about the 3.50? well "y" at $3.50 is 3.50y

whatever amount that was, TOTALed 59.50
thus

\(\Large \bf 5x + 3.50y = 59.50\)

Answer 2

You need to make a system of equations :)
x = number of times she deposited 5 dollars
y = number of times she deposited $3.50
Equation One: 5x + 3.5y = 59.5
Equation Two: x + y = 14
I'm using the substitution method, because I find that to be the fastest.
For equation two, subtract y from both sides ( (x+y)-y = 14 - y)
You'll get x = 14 - y
Substitute the new equation two in for x in equation one:
5(14-y) + 3.5y = 59.5
70 - 5y + 3.5y = 59.5
70 - 1.5y = 59.5
-1.5y = -10.5
-1.5y/-1.5 = -10.5/-1.5
y = 7
Plug in y for the original equation two,
x + 7 = 14
x = 7
Mia deposited $5 seven times and $3.50 seven times.

Answer 3

In other words:
x number of deposits for $5
and y ......................................... for $3.5
total deposits x+y=14
5x number of deposit for $5
3.5y ....................... for $3.50
then the second equation is
5x+3.5y=59.50

Answer 4

oh you gave the other guy a medal. I wasted my time! :(