Find the price of potatoes per kilogram if, when the price rises by 5c per kg, I can buy 1 less kg for $2.10.

[INeedHelpWithMyMath]

Hi,

I've tried to solve this question but I'm not really getting anywhere, was wondering if you guys could help. What I tried was to form an equation relating the price/kg, total price, and kg. I made the equation:

(a+5)(x-1)=210

Where a= price/kg
and x= kg

I tried to make an equation for the original price/kilogram, but with the information in the question all I can reach is an expression:

(a)(x)=total price

With the same variables.

Thank you in advance for any help!

 

[MarkFL]

Hello, and welcome to FMH!

Let's let \(a\) be the price of potatoes per kilogram and \(x\) be the number of kilograms that can be bought for $2.10. Thus, we may state:

[MATH]ax=210[/MATH]
Now, when the price increases by 5 cents, the number of kilograms that can be purchased for $2.10 decreases by 1:

[MATH](a+5)(x-1)=210[/MATH]
Since we are asked to find \(a\), let's substitute for \(x\) from the first equation into the second:

[MATH](a+5)\left(\frac{210}{a}-1\right)=210[/MATH]
Can you proceed to solve this equation for \(a\)?

 

[MarkFL]

To follow up, multiply the equation by \(a\):

[MATH](a+5)(210-a)=210a[/MATH]
Expand the LHS:

[MATH]210a-a^2+1050-5a=210a[/MATH]
Arrange in standard form:

[MATH]a^2+5a-1050=0[/MATH]
Factor:

[MATH](a+35)(a-30)=0[/MATH]
Discarding the negative root, we find:

[MATH]a=30[/MATH]
Let's check our answer...if the price per kg is 30 cents, then we can by 7 kg with 210 cents. If the price rises by 5 cents to 35 cents, then 210 cents will buy us 6 kg, which is 1 less than 7. So, it checks out.

 

[Steven G]

Hi,

I've tried to solve this question but I'm not really getting anywhere, was wondering if you guys could help. What I tried was to form an equation relating the price/kg, total price, and kg. I made the equation:

(a+5)(x-1)=210

Where a= price/kg
and x= kg

I tried to make an equation for the original price/kilogram, but with the information in the question all I can reach is an expression:

(a)(x)=total price

With the same variables.

Thank you in advance for any help!

Your definition for x is not clear at all. You should say that x is the number of kg so your cost will be 210