"Products" Math Problem

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Kristina123

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Three cards are lined up on a table. Each card has a letter printed on one side and a positive number printed on the other side. One card has an R printed on it, one card has a G printed on it, and one card has a B printed on it. The number side of each card is facedown on the table.

The following is known about the three concealed numbers:

(i) the product of the number on the card with an R and the number on the card with a G equals the number on the card with a B;
(ii) the product of the number on the card with a G and the number on the card with a B is 180; and
(iii) five times the number on the card with a B equals the number on the card with a G.

Determine the product of the numbers on the three cards.

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I understand that "product" is the result of multiplying. However, I don't understand what the 3 points mentioned above is trying to tell me. It first says that the product of the number on the card with a G and the number on the card with a B is 180, which tells me that the number concealed in card G and B is 180. But in point 3, it says that the number on card G is five times the number on card B. I'm so confused. Card G is not 180? I don't even know if my explanation on where I'm getting stuck even makes sense to you guys. Can someone interpret the meaning of these 3 points and help me start off the problem.
 
Kristina123 said:
Three cards are lined up on a table. Each card has a letter printed on one side and a positive number printed on the other side. One card has an R printed on it, one card has a G printed on it, and one card has a B printed on it. The number side of each card is facedown on the table.
The following is known about the three concealed numbers:
(i) the product of the number on the card with an R and the number on the card with a G equals the number on the card with a B;
(ii) the product of the number on the card with a G and the number on the card with a B is 180; and
(iii) five times the number on the card with a B equals the number on the card with a G.
Determine the product of the numbers on the three cards.
Click to expand...
Lets say that \(\displaystyle r\) is the number on the card marked \(\displaystyle \mathcal{R}\), \(\displaystyle g\) is the number on the the card marked \(\displaystyle \mathcal{G}\), and \(\displaystyle b\) is the number on the card marked \(\displaystyle \mathcal{B}\).
From the given: \(\displaystyle r\cdot g=b \\g\cdot b=180\\5\cdot b = g\)
Can you solve the equations in three unknowns?
 
pka said:
Lets say that \(\displaystyle r\) is the number on the card marked \(\displaystyle \mathcal{R}\), \(\displaystyle g\) is the number on the the card marked \(\displaystyle \mathcal{G}\), and \(\displaystyle b\) is the number on the card marked \(\displaystyle \mathcal{B}\).
From the given: \(\displaystyle r\cdot g=b \\g\cdot b=180\\5\cdot b = g\)
Can you solve the equations in three unknowns?
Click to expand...
I'm still stumped
 
Kristina123 said:
I'm still stumped
Click to expand...
Well you need to know that I will not work this question for you.
If You use equation #1 into #3 we get \(\displaystyle 5(r\cdot g)=g\)

Now this may sound harsh to you, but it is meant to help you,
If after seeing the above you are still stumped, then you a beyond any help we may give.
If we give you the answer, then you have learned nothing.
So your need a face-to-face sit down with a tutor.
 
pka said:
Well you need to know that I will not work this question for you.
If You use equation #1 into #3 we get \(\displaystyle 5(r\cdot g)=g\)

Now this may sound harsh to you, but it is meant to help you,
If after seeing the above you are still stumped, then you a beyond any help we may give.
If we give you the answer, then you have learned nothing.
So your need a face-to-face sit down with a tutor.
Click to expand...
I want to find the answer myself. What is the next step that you are asking me to do?
 
Kristina123 said:
Three cards are lined up on a table. Each card has a letter printed on one side and a positive number printed on the other side. One card has an R printed on it, one card has a G printed on it, and one card has a B printed on it. The number side of each card is facedown on the table.

The following is known about the three concealed numbers:

(i) the product of the number on the card with an R and the number on the card with a G equals the number on the card with a B;
(ii) the product of the number on the card with a G and the number on the card with a B is 180; and
(iii) five times the number on the card with a B equals the number on the card with a G.

Determine the product of the numbers on the three cards.

---------

I understand that "product" is the result of multiplying. However, I don't understand what the 3 points mentioned above is trying to tell me. It first says that the product of the number on the card with a G and the number on the card with a B is 180, which tells me that the number concealed in card G and B is 180. But in point 3, it says that the number on card G is five times the number on card B. I'm so confused. Card G is not 180? I don't even know if my explanation on where I'm getting stuck even makes sense to you guys. Can someone interpret the meaning of these 3 points and help me start off the problem.
Click to expand...
You say that you understand product means to multiply but then you do not do that.
You are told that the product of the number on the card with a G and the number on the card with a B is 180. So why should G or B equal 180. Their product equals 180. That is G*B = 180


(i) the product of the number on the card with an R and the number on the card with a G equals the number on the card with a B means G*R=B
(ii) the product of the number on the card with a G and the number on the card with a B is 180 means G*B=180
(iii) five times the number on the card with a B equals the number on the card with a G means 5B=G

You know another way of writing G (it is 5b) so put this new way of writing G into G*B=180 giving us (5B)*B = 180 or 5B^2 = 180. So what does B^2 equal. Hint: it is the answer to 5 times what equals 180
 
Kristina123 said:
Is it [MATH]180 \div g = b[/MATH] ?
Click to expand...
Yes, so now plug this new way of writing b into another equation. What do you get?
Also, instead of using 180 \(\displaystyle \div g\), you can write it as a fraction as\(\displaystyle \dfrac {180}{g}\)
 
Jomo said:
You say that you understand product means to multiply but then you do not do that.
You are told that the product of the number on the card with a G and the number on the card with a B is 180. So why should G or B equal 180. Their product equals 180. That is G*B = 180


(i) the product of the number on the card with an R and the number on the card with a G equals the number on the card with a B means G*R=B
(ii) the product of the number on the card with a G and the number on the card with a B is 180 means G*B=180
(iii) five times the number on the card with a B equals the number on the card with a G means 5B=G

You know another way of writing G (it is 5b) so put this new way of writing G into G*B=180 giving us (5B)*B = 180 or 5B^2 = 180. So what does B^2 equal. Hint: it is the answer to 5 times what equals 180
Click to expand...
[MATH]B^2 = 36[/MATH]
 
Kristina123 said:
I want to find the answer myself. What is the next step that you are asking me to do?
Click to expand...
Well that is a simple question to answer.
SOLVE \(\displaystyle 5(r\cdot g)=g\) for \(\displaystyle r\).
 
Kristina123 said:
[MATH]5 \cdot r = g[/MATH], and g is 30 i believe
so r is 6?
Click to expand...
No, you are NOT told that 5*r =g. Where does it say that? It says that (5*r)*g=g. 5r is unknown, but we know that when we multiple it by g we get g. Well what do you multiply g by to get g? The answer to that question is what 5r must equal.
 
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