Price of Mango and Guava Mix: Does Size Matter?

[athamz]

Homework Statement

A bag containing a mixture of 6 mangoes and 12 guavas sold for $234. A smaller bag containing 2 mangoes and 4 guavas sold for $77. An alert shopperasked the salesclerk if it was better to purchase the larger bag. The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

You appear to have forgotten something:

The Attempt at a Solution

 

[athamz]

I am sorry, but I don't know how and when to start, could you help me?​

 

[Hootenanny]

I am sorry, but I don't know how and when to start, could you help me?​

What is the ratio between the pieces of fruit and prices in each case?

 

[Ray Vickson]

Homework Statement

A bag containing a mixture of 6 mangoes and 12 guavas sold for $234. A smaller bag containing 2 mangoes and 4 guavas sold for $77. An alert shopperasked the salesclerk if it was better to purchase the larger bag. The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?

Homework Equations

The Attempt at a Solution

You have two equations in the two unknowns m = price per mango and g = price per guava. What happens when you start to solve them?

RGV

 

[Mark44]

A bag containing a mixture of 6 mangoes and 12 guavas sold for $234. A smaller bag containing 2 mangoes and 4 guavas sold for $77. An alert shopperasked the salesclerk if it was better to purchase the larger bag. The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?

If "$" means USD, that is some VERY expensive fruit.

 

[HallsofIvy]

That was my thought!

 

[athamz]

I have this Equation using x and y variables. x for price per mango and y for price per mango. so the equations are 6x + 12y = 234 and 2x + 4y = 77..

But I did not get the value for the x and y using that two equations...

It says in the problem that the sales clerk was wrong..

I think there's something wrong with the equations..

Help me please...

 

[ArcanaNoir]

How many small bags of fruit equal one big bag of fruit in number of fruit? (ignore the cost of the bags) once you know that, you should be able to tell which bag is a better deal.

 

[athamz]

How many small bags of fruit equal one big bag of fruit in number of fruit? (ignore the cost of the bags) once you know that, you should be able to tell which bag is a better deal.

But How can I do that? can you give me the first step?

 

[symbolipoint]

athamz wrote problem description:

A bag containing a mixture of 6 mangoes and 12 guavas sold for $234. A smaller bag containing 2 mangoes and 4 guavas sold for $77. An alert shopperasked the salesclerk if it was better to purchase the larger bag. The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?

Notice the ratio of mango to guava is the same for each bag. This ratio is 1 mango to 2 guava. You are then really interested in price as number of fruit for each dollar of cost. This becomes really just a one-step problem in two parts; large bag part, and small bag part.

How many pieces of fruit in the large bag? What is ratio of number of fruit to price of large bag?
How many pieces of fruit in the small bag? What is the ratio of number of fruit to price of small bag?

 

[Mark44]

I have this Equation using x and y variables. x for price per mango and y for price per mango. so the equations are 6x + 12y = 234 and 2x + 4y = 77..

Don't you notice something about these two equations?

If two mangoes and four guavas cost $77, how much would you expect to pay for four mangoes and eight guavas?

It says in the problem that the sales clerk was wrong..

I think there's something wrong with the equations..

No, your equations are fine, except how you defined y - it should be the price per guava.

Help me please...

 

[athamz]

athamz wrote problem description:


Notice the ratio of mango to guava is the same for each bag. This ratio is 1 mango to 2 guava. You are then really interested in price as number of fruit for each dollar of cost. This becomes really just a one-step problem in two parts; large bag part, and small bag part.

How many pieces of fruit in the large bag? What is ratio of number of fruit to price of large bag?
How many pieces of fruit in the small bag? What is the ratio of number of fruit to price of small bag?

Can you give me the equation? I don't know how to form equation...

 

[Mark44]

We are NOT here to do your work for you. We are happy to help you and steer you in the right direction, but you need to do most of the work. If you go back and reread what people have written here, you should be able to do this problem.

 

[quietrain]

if 2 nuggets cost $10,

and 4 nuggets cost $18, which is the better deal?

assuming you like eating that is..

 

[HallsofIvy]

Reread your original problem. "The clerk was not sure, but said that it really made no difference because the price of each package was based on the same unit price for each kind of fruit. Why was the clerk wrong?"

That does NOT ask you to find the price of each fruit in each package- only to say why it was not the same for the two packages. That is, x and y cannot be the same in the two equations. You said,
"I did not get the value for the x and y using that two equations...

I think there's something wrong with the equations.."

Yes, that's the whole point of the problem!