You are here:

# Algebra/Algebra

Question
There were 310 phones and tabs for sale in a shop.All the phones in the shop cost \$2484 more than all the tabs. After 1/3 of the phones and 10/11 of the tabs were sold, there were thrice as many phones as tabs left.If each phone cost \$714 more than each tab,how much did each tab cost?

Let P be the number of phones and T be the number of tabs.
Let x be the price of a phone and y be the price of a tab.

There were 310 phones and tabs for sale in a shop, so P + T = 310
and P and T are both integers.

All the phones in the shop cost \$2484 more than all the tabs, so Px - Ty = 2484.

After 1/3 of the phones and 10/11 of the tabs were sold, there were thrice as many phones as tabs left. With the amount sold, that leave 2P/3 and T/11,
so this says that 2P/3 = 3(T/11).

If each phone cost \$714 more than each tab sounds a little fishy,
but what it says is that x = y + 714.  The reason it sounds fishy is that the price of most phones is far under \$714.

The equations are, then,
P + T = 310,
Px - Ty = 2484,
2P/3 - 3T/11 = 0, and
x - y = 714.

Using the 1st equation, it can be rewritten as P = 310 - T.
Putting this into the 3rd equation gives 2(310-T)/3 - 3T/11 = 0.
Multiplying this out gives 620/3 – 2T/3 - 3T/11 = 0.
This is the same as 2T/3 + 3T/11 = 620/3.
Multiplying by 33 gives 22T + 9T = 6820.
That is the same as 31T = 6820.
That gives T=220.

Using the 1st equation again, this says that P = 90.

Putting these values into the 2nd equation gives 90x – 220y = 2484.
The 4th equation can be converted to x = 714 – y.
Putting this back in the prior equation gives 90(714-y) – 220y = 2484.
That multiplies out to 64260 – 90y – 220y = 2484.
This says that 61776 = 310y, so y = \$2059.20, and that's what the question is asking for.

If we look a little farther, however, putting that into the 4th equation gives
x – 2059.2 = 714, so x = \$2773.20.  That seems a little expensive for a phone,
but that’s what I get from what’s given.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thankyou very much for your help.

Algebra

Volunteer

#### Scott A Wilson

##### Expertise

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

##### Experience

I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Publications
Documents at Boeing in assistance on the manufacturiing floor.

Education/Credentials
MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

Past/Present Clients
Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.