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need Algebra word problem help!!!!!


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:confused:We are on Foerster's Algebra I, lesson 7-10, #9

 

A gas station has just raised its prices. The attendant resets the pump but forgets to record the old prices. Rather than revealing her forgetfulness, she consults yesterday's sales report. She finds that 450 liters of regular and 320 liters of unleaded were sold for a total of $384.83. Regular was 5 cents per liter cheaper than unleaded. What were the two prices per liter yesterday?

 

 

We are solving problems using two variables.

 

This is what I have so far:

 

x = regular

y = unleaded

 

450 x + 320 y = 384.83

 

What do you do about the 5 cents cheaper? ( y - 5???)

 

Can you walk me step by step throug this?

 

 

Thanks,

Melissa

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:confused:We are on Foerster's Algebra I, lesson 7-10, #9

 

A gas station has just raised its prices. The attendant resets the pump but forgets to record the old prices. Rather than revealing her forgetfulness, she consults yesterday's sales report. She finds that 450 liters of regular and 320 liters of unleaded were sold for a total of $384.83. Regular was 5 cents per liter cheaper than unleaded. What were the two prices per liter yesterday?

 

 

We are solving problems using two variables.

 

This is what I have so far:

 

x = regular

y = unleaded

 

450 x + 320 y = 384.83

 

What do you do about the 5 cents cheaper? ( y - 5???)

 

Can you walk me step by step throug this?

 

 

First you are right with the initial basic idea....take 450X +320Y = 384.83 but then notice that the cost of regular, X, is .05 less than the price of Y, so substitute Y-.05 for X thus:

 

450X + 320Y = 384.83 becomes

 

450(Y-.05) +320Y = 384.83 then multiply through by 450

 

450Y - 22.50 + 320Y = 384.83 then add the 22.50 to the other side...

 

450Y + 320Y = 407.33 combine like terms

 

770Y = 407.33 then divide by 770

 

Y=.529 cents this is the price of unleaded.

 

subtract .529 - .05 = .479 cents for regular

 

Check

 

450 X .479 = 215.55 regular sold

 

320 X .529 = 169.28 unleaded sold

 

215.55 + 169.28 = 384.83 total sales.

 

HTH

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