MHB What is the cost of ten bananas and ten pears?

[mathdad]

Three bananas and two pears cost 95p. Five bananas and three pears cost £1.51. What is the cost of ten bananas and ten pears?

 

[Greg]

Using the given information we have

$$3b+2p=95$$

and

$$5b+3p=151$$

where $b$ represents the cost of bananas and $p$ represents the cost of pears. Do you see how the equations above were formed? Can you solve this system of equations?

 

[mathdad]

Re: Bananas & Pears

Using the given information we have

$$3b+2p=95$$

and

$$5b+3p=151$$

where $b$ represents the cost of bananas and $p$ represents the cost of pears. Do you see how the equations above were formed? Can you solve this system of equations?

I had no idea that a system of linear equations is hidden in the words of this problem.

- - - Updated - - -

This is my biggest problem. I have such a hard time creating an equation from written information in applications. This is my biggest weakness in math. I am hoping to overcome this set back through the help of caring mathematicians.

 

[Greg]

I suspect 151 should be 150.

 

[mathdad]

I suspect 151 should be 150.

It is possible that 151 should be 150 but the problem as stated has £1.51.

 

[HallsofIvy]

Three bananas and two pears cost 95p. Five bananas and three pears cost £1.51. What is the cost of ten bananas and ten pears?

You say "I have such a hard time creating an equation from written information in applications." Here is how I would think about it:

To determine "the cost of ten bananas and ten pears" we should first determine the cost of one banana and the cost of one pear. We can first let "b" be the cost of a single banana and "p" be the cost of a single pear in pence.

"Three bananas and two pears cost 95 p".
The cost of one banana is b so the cost of three bananas is 3b. The cost of one pear is p so the cost of two bananas s 2p. The cost of "three bananas and two pears" is 3b+ 2p= 95

"Five bananas and three pears cost 151 p"
As above, the cost of five bananas is 5b and the cost of three pears is 3p so the cost of "five bananas and three pears" is 5b+ 3p= 151.

the two equations are 3b+ 2p= 95 and 5b+ 3p= 151. Once you have solved those equations for b and p, calculate 10b+ 10p to answer the question.

(My sole criticism of greg1313's post is that he did not say that "p" represented the cost of a pear or that "b" represented the cost of a banana.)

 

[Greg]

(My sole criticism of greg1313's post is that he did not say that "p" represented the cost of a pear or that "b" represented the cost of a banana.)

In common English I stated exactly that but then I'm a little old.

Three bananas and two pears cost 95p. Five bananas and three pears cost £1.51. What is the cost of ten bananas and ten pears?

I have a suggestion. For 151 pence equaling the cost of five bananas and three pears, let's make it 150 pence. Then the system has integer solutions and is much easier to work with. After you get comfortable with that, we can revisit our friend 151. Ok?

 

[mathdad]

Three bananas and two pears cost 95. Five bananas and three pears cost \$1.50. What is the cost of ten bananas and ten pears?

3b+2p= 95...A
5b+3p=150...B

3b + 2p = 95

3b = 95 - 2p

b = (95 - 2p)/3...Plug into B.

5[(95 - 2p)/3] + 3p = 150

So, p = 25 cents.

Plug p = 25 into either A or B.

5b + 3p = 150

5b + 3(25) = 150

5b + 75 = 150

5b = 150 - 75

5b = 75

b = 75/5

b = 15, that is, 15 cents.

Ten Bananas = 10(0.15) or \$1.50.

Ten pears = 10(0.25) or \$2.50.

 

[Greg]

Ten Bananas = 10(0.15) or \$1.50.

Ten pears = 10(0.25) or \$2.50.

So what is the "cost of ten bananas and ten pears"? "Cost" is singular. Use the monetary units stated in the problem. ;)

 

[mathdad]

So what is the "cost of ten bananas and ten pears"? "Cost" is singular. Use the monetary units stated in the problem. ;)

1. I do not know that particular monetary unit.

2. Ten bananas and ten pears = 1.50 + 2.50 or 4.00.

 

[Greg]

1. I do not know that particular monetary unit.

You used it in your original post.

 

[mathdad]

Ok. I'll look into the monetary units later or tomorrow.

 

[HallsofIvy]

Re: Bananas & Pears

1. I do not know that particular monetary unit.

Yes, you do! The original problem, which you posted said "Five bananas and three pears cost £1.51"

2. Ten bananas and ten pears = 1.50 + 2.50 or 4.00.

Ten bananas and ten pears cost £1.50+ £2.50 or £4.00

 

[mathdad]

Thank you everyone. Moving on...