is problem 1 correct? system of equations for word problems

[curelnew]

A. Write a system of equtions for problems.
B. How many of each type does he have?

Problem 1.
Alex has 80 coins, all are either quarters or nickels. Total value of coins is $14.95.
x+y=80
.25x+.05y=14.95
x=-y+80
.25(-y+80)+.05y=14.95
-.25y+20+.05y=14.95
-.2y+20=14.95
-.2y=-20+14.95
-.2y=-5.05
y=25.25

x+25.25=80
x=-25.25+80
x=54.75


Problem 2
Don has 42 stamps, mixture of 37-cent stamps and 23-cent stamps. (This is all the info)
x+y=42
y=-x+42
x+-x+42=42
42=42
? not right

 

[Mrspi]

Re: system of equations for word problems

A. Write a system of equtions for problems.
B. How many of each type does he have?

Problem 1.
Alex has 80 coins, all are either quarters or nickels. Total value of coins is $14.95.
x+y=80
x+y=$14.95
x=-y+80
x+(-y+80)=14.95
x-y+80=14.95
x=y-80+14.95
?

Problem 2
Don has 42 stamps, mixture of 37-cent stamps and 23-cent stamps. (This is all the info)
x+y=42
y=-x+42
x+-x+42=42
42=42
? not right

You should always start problems like these by NAMING THINGS. You've used "x" and "y" but you have NOT said what those variables stand for....if you don't know what they stand for, you're very likely to use them incorrectly. (Which is what has happened in both of your problems).

For problem 1, what do x and y represent? Is x the NUMBER of one type of coin? Is x the VALUE of some of the coins?

I'd start like this:

let x = number of quarters
let y = number of nickels

We are told that there are 80 coins in all, so the number of quarters PLUS the number of nickels must be 80 coins:

x + y = 80

We are also told that the total value of the coins is $14.95. Can we use the equation "x + y = 14.95"?? No...we can't, because x and y represent the NUMBERS of quarters and nickels, and not the value of those coins.

A quarter is worth $0.25. If you have x quarters, and each one of them is worth $0.25, then the value of those x quarters would be $0.25 * x, or 0.25x. You can write a similar expression for the value of y nickels...with each nickel being worth $0.05. And then you can write an equation to say "value of the quarters plus value of the nickels is 14.95" That equation will be

0.25x + 0.05y = 14.95

Use these two equations as your system:

x + y = 80
0.25x + 0.05y = 14.95

See if that gives you an answer that "checks."

You'll need to do something similar for problem 2....you have to consider the NUMBER of each of two kinds of stamps. You'll also have to consider what those stamps are worth. So, one equation in your system will deal with how many stamps there are, and one equation will deal with how much money the stamps are worth.

 

[Deleted member 4993]

When I solve these problems - where I have to name variables - I try to choose variable names that associate with the variable.

Thus I choose:

# of quarters = Q

# of nickels = N

Then continue as Mrs? has shown you.

This is a good habit - choosing relevant variable name - that will be useful if start doing computer programming.

 

[wjm11]

Problem 1.
Alex has 80 coins, all are either quarters or nickels. Total value of coins is $14.95.
x+y=80
.25x+.05y=14.95
x=-y+80
.25(-y+80)+.05y=14.95
-.25y+20+.05y=14.95
-.2y+20=14.95
-.2y=-20+14.95
-.2y=-5.05
y=25.25

x+25.25=80
x=-25.25+80
x=54.75


Problem 2
Don has 42 stamps, mixture of 37-cent stamps and 23-cent stamps. (This is all the info)
x+y=42
y=-x+42
x+-x+42=42
42=42
? not right

For problem 1, consider that it is not possible to have fractional numbers of coins. I would expect the answers to be whole numbers. It would be a good idea to see if you've copied the problem info correctly.

For problem 2, what you have discovered is that it's usually not possible to solve for two variables if you have only one equation. Once again, check the problem info to see if you might have missed something (like the total value of the stamps).