word problem

[paige1923]

I need to know how to translate this word problem into an equation.
a. The sales representative informs you that there are 56 houses for sale with two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.
x+y=56is this right
b. The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part a.
x+3y=56

 

[mmm4444bot]

x + y = 56 This is correct.

x + 3y = 56 This is silly.

If x homes plus y homes is a total of 56 homes, then how could tripling the number y still lead to a sum of 56?

The only way that could happen is if y = 0.

But that doesn't jive with part (b) because 0 is not three times bigger than 56!

Before using them, you first need to define the symbols x and y. Write it down.

Let x = the number of homes with floor plan 1

Let y = the number of homes with floor plan 2

Part (b) tells us that there are more homes available with floor plan 2.

"three times as many homes available with the second floor plan than the first"

This statement is a relationship between x and y that does not involve their total; in other words, the equation that you write for part (b) does not involve the number 56.

You multiplied y by 3. We don't triple the value of y because it's already the bigger number, yes? (Read the quote in green above, again.)

To say that y is three times bigger than x means that we would need to triple x to get the same value as y.

Does that make sense?

So, there is your equation.

Tripling x results in y.

 

[paige1923]

thank you I knew I was wrong I was just cofused on haw to write the equation.You answer makes sense

 

[precious]

I am working on the same problem. I wrote x+y=56, then for the next question it states y has three more time the amount of homes. I can only conclude that we need to know what y is to know the amount, but even with your explanation I am in a quandry as I take it to mean x+3(y)=56. I am still unsure as to how to write it? The next question is looking for an equation to represent $7,200,000. worth of homes with model A. priced at $200,000. and B. priced at $175,000. All I know is x + y= $7,200,000. We need to find how many of each as before. Still not sure on how to write this?

 

[mmm4444bot]

?

I take it to mean x + 3(y) = 56 This is not correct. We are told that x + y equals 56, not x + 3y.

The given exercise makes the following statement:

there are three times as many homes available with the second floor plan than the first

This statement says nothing about the total number of homes. This statement is only a comparison between two numbers. Specifically, those two numbers that we've decided to call x and y.

The number y is three times larger than the number x.

In other words, since y is the larger number, we would need to triple the number x to get the same value.

3x = y

x + y = 56

This is a system of two equations. It has one solution.

?

All I know is x + y = $7,200,000. This equation indicates that x and y represent dollar amounts. Is that what you are thinking?

For the part of your exercise that involves money, we can write the following.

Let A = the number of $200,000 homes

Let B = the number of $175,000 homes

Now, we can use the symbols A and B to write some expressions.

An expression that models the total value of the homes with floor plan A is 200000A .

Does that make sense?

We simply multiply $200,000 times the number of homes that are each worth that much.

Likewise, an expression that models the total value of the homes with floor plan B is 175000B .

The sum of these two dollar amounts equals 7200000, yes?

If you need more help writing this sum as an equation, please show what you tried or explain what you're thinking.

?