Linear Equation Problem Solving

[milesprower64]

Hello Everyone!
I'm having trouble trying to figure out this problem solving question that deals with linear equations.

Express as a system of linear equations and then solve

Sol's Club Discount Warehouse has two membership plans. Under plan A the customer pays a $50 annual membership and 85% of the manufacturer's recommended list price. Under plan B the annual membership fee is $100 and the customer pays 80% of the manufacturer's recommended list price. How much merchandise, in dollars, would one have to purchase to pay the same amount under both plans?

I'm having a hard time trying to figure out how to setup up the linear equations in order to find the solution. Its very confusing. If anyone has a idea please tell me.
Thank You!

~MilesPrower64~[/b]

 

[tkhunny]

You are NOT without weapons against such problems. Start simply and move forward logically.

Rule #1 - Name Stuff.

Name what?

What does it want?

"How much merchandise, in dollars, would one have to purchase to pay the same amount under both plans?"

X = merchandise, in dollars, would one have to purchase to pay the same amount under both plans.

Translate the problem statement hints:

Plan A
"$50 annual membership and 85% of the manufacturer's recommended list price"
$50 + 0.85*X

Plan B
"annual membership fee is $100 and the customer pays 80% of the manufacturer's recommended list price"
$100 + 0.80*X

"pay the same amount under both plans"
$50 + 0.85*X = $100 + 0.80*X

Can you solve?

 

[milesprower64]

Ooooh! Okay, After showing my work, I got x = $1,000

50+0.85x = 100+0.8x

50+(-50)+0.85x = 100+0.8x+(-50)

0.85x = 50+0.8x

0.85x+(-0.8x) = 50+0.8x+(-0.8x)

0.05x = 50

0.05x/0.05 = 50/0.05

x = 1,000
______________
The method you showed, is quite different from what the textbook's method that I'm using. Such as,

(1)y = x + 5
(2)y = 2x + 4

Thats the kind of linear equations that I was taught.
Thank You for all of your help tkhunny! I appreciate it.

~MilesPrower64~

 

[tkhunny]

50+0.85x = 100+0.8x

The method you showed, is quite different from what the textbook's method that I'm using. Such as,

(1)y = x + 5
(2)y = 2x + 4

We could have done that.

1) y = 50+0.85x
2) y = 100+0.8x

Since we wish to know 'x', my first move would be to notice that both expressions equal 'y'. This leads to: 50+0.85x = 100+0.8x

It is likely that you book is not trying to teach you how to think about it. That is my goal.

If the problem had asked for the total amount paid, such that the two are equal, I would have solved for 'y', instead. This is why we write down clear definitions and reread the problem statement a couple of times, to make sure we know what it wants and what we are doing.

Good deal!