Question 1185563
the change jar has 60 coins composed of pennies and dimes only.


you can work this problem in cents, or you can work this problem in dollars.


it makes a difference.


if you work this problem in dollars, then your equations are:


x + y = 60
.10x + .01y = 3.57


multiply both sides of the first equation by .10 and leave the second equation as is to get:


.10x + .10y = 6
.10x + .01y = 3.57


subtract the second equation from the first to get:


.09y = 2.43


solve for y to get:


y = 2.43 / .09 = 27


since x + y = 60, then x = 33.


confirm by replacing x and y in the original equations with 33 and 27 to get:


x + y = 33 + 27 = 60
.10x + .01y = .10*33 + .01*27 = 3.3 + .27 = 3.57


both of these equations confirm the value of x and y are good.


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if  you work this problem in cents, then your equations are:


x + y = 60
10x + y = 357


multiply both sides of the first equation by 10 and leave the second equation as is to get:


10x + 10y = 600
10x + y = 357


subtract the second equation from the first to get:


9y = 243


solve for y to get:


y = 243/9 = 27


since x + y = 60 then x = 33.


confirm the value are good by replacing x and y with 33 and 27.


x + y = 33 + 27 = 60
10x + y = 10*33 + 27 = 330 + 27 = 357


values of x and y are confirmed to be good.


the key is to determine whether you want to solve the problem in cents or in dollars.


if cents, then 3.57 becomes 357 cents and dimes becomes 10x and pennies become y


if dollars, then 3.57 is left as is and dimes becomes .10x and pennies become .01y


remember, x is the number of dimes and y is the number of pennies.


.10x gives you the value of the dimes in dollars.
.01y gives you the value of the pennies in dollars.


10x gives you the value of the dimes in cents.
y gives you thje value of the pennies in cents.
keep in mind that y means 1 * y which can also be shown as 1y.