# Math Help - Word problem - with confusing phrasing

1. ## Word problem - with confusing phrasing

Last week, Dolly bought x kg of grade B coffee powder for $12. If she bought grade A coffee powder instead, she would get 200 g less for$12. This week, the price of coffee powder for both grades increased by $5.00 per kg. If Dolly buys grade A coffee powder instead of grade B coffee powder, she will get 120 g less for$12.

Find how much grade B coffee powder Dolly bought last week.

I am thinking on the lines of quantity for week 2 x unit price for week 2 = 12 will yield a quadratic equation to solve.

But, I am confused with the second half of the problem. Does the 120 g less mean that she will get grade A coffee less that grade A for previous week or less that grade B this week?

Edit: Sorry forgot the question part!

2. Originally Posted by mathguy80
Last week, Dolly bought x kg of grade B coffee powder for $12. If she bought grade A coffee powder instead, she would get 200 g less for$12. This week, the price of coffee powder for both grades increased by $5.00 per kg. If Dolly buys grade A coffee powder instead of grade B coffee powder, she will get 120 g less for$12.

I am thinking on the lines of quantity for week 2 x unit price for week 2 = 12 will yield a quadratic equation to solve.

But, I am confused with the second half of the problem. Does the 120 g less mean that she will get grade A coffee less that grade A for previous week or less that grade B this week?

1. x := amount of grade A coffee
a:= old price per kg grade A coffee
a + 5 := new price per kg grade A coffee

2. According to the text you know:

$(x-0.2) \cdot a = 12$

$(x-0.2-0.12) \cdot (a+5)=12$

3. Determine x from the 1st equation and replace the variable x in 2nd equation by this term. Solve for a.

3. Thanks @earboth for your help.

I forgot the most important part of the question, Sorry! The question is, Find how much grade B coffee powder Dolly bought last week.

I am a little confused about your use of x. The question has the variable x with x Kg of grade B coffee powder. Is this a different variable x? I solved the equation assuming a different x. And got x = 40 kg, so corresponding grade B would be 40.2 Kg. This doesn't fit the answer at the back, which is x = 0.8 Kg. Did i solve it right?

4. Originally Posted by mathguy80

I forgot the most important part of the question, Sorry! The question is, Find how much grade B coffee powder Dolly bought last week.

I am a little confused about your use of x. The question has the variable x with x Kg of grade B coffee powder. Is this a different variable x? I solved the equation assuming a different x. And got x = 40 kg, so corresponding grade B would be 40.2 Kg. This doesn't fit the answer at the back, which is x = 0.8 Kg. Did i solve it right?
1. You are absolutely right: The x denotes the amount of grade B coffee.

2. From the 1st equation (of post #2) you'll get: $x = \dfrac{12}a + 0.2$

3. Replace the variable x by this term:

$\left(\dfrac{12}a + 0.2-0.2-0.12\right)(a+5)=12~\implies~-0.12a^2-0.6a+60=0$

4. Solve for a. I've got a = \$20 per kg of B-coffee(The negative solution isn't very plausible here!)

5. Then $x = 0.6 + 0.2 = 0.8$. So Dolly bought 0.8 kg B-coffee and she would have got 0.6 kg A-coffee for the same price.

5. Got it! I also had a mistake in my quadratic solution. After fixing it got a = -25 (rejected) and a = 20.
Then got x = 0.8.

Excellent. Thanks for clearing this up. I went from to in a few hours. It was very helpful!