Problem to discuss: January

Here is a problem that I found in a magazine, let's have some fun and see if we can come up with several approaches on how we could solve this puzzle:

A single plate setting includes a dinner plate, salad plate, soup bowl, and cup and saucer.  The dinner plate costs $3 more than the salad plate.  The cup and saucer costs half the price of the salad plate.  The soup bowl costs $6.  If an entire service for 8 people costs $352, what is the cost of a single dinner plate?

If you solve it quickly, try thinking of another way to solve it - can you graph it, draw it, diagram it, etc.  Let's see how many ways we can get to the solution of this problem and then share the ways with each other.

Time to get our math nerd on,

Brooke 

#MTBos #ANNmath 

Comments

The cup and saucer costs half the price of the salad plate

Does this mean that the combination of the cup and saucer together costs half the price or does each the cup cost half the price and the saucer also costs half the price?

 

Here are the two most intuitive solutions for me.

 

A single plate setting includes a dinner plate, salad plate, soup bowl, and cup and saucer.  The dinner plate costs $3 more than the salad plate.  The cup and saucer costs half the price of the salad plate.  The soup bowl costs $6.  If an entire service for 8 people costs $352, what is the cost of a single dinner plate?

If you solve it quickly, try thinking of another way to solve it - can you graph it, draw it, diagram it, etc.  Let's see how many ways we can get to the solution of this problem and then share the ways with each other.

Algebra and check

Dinner plate = x+3

Salad plate = x

Soup bowl = 6

Cup and Saucer = x/2

Setting = (x+3) + x + 6 + x/2

352 = 8((x+3) + x + 6 + x/2)

352 = 8((5/2)x +9)

352 = 20x + 72

280 = 20x

14 = x

$17 = x+3 = dinner plate

 

Guess and check using rates, and check

Since 8 x 40 = 320 and 8 x 50 = 400 the cost of an individual setting should be between $40 and $50.  We can divide to find the exact number 320/8 = $44

Try $10 for a dinner plate

Dinner plate = 10

Salad plate = 10-3 = 7

Soup bowl = 6

Cup and Saucer = 7/2 = 3.5

Setting = 10 + 7 + 6 +3.5 = 26.5

That’s too low.  Let’s try one dollar more.

Try $11 for a dinner plate

Dinner plate = 11

Salad plate = 11-3 = 8

Soup bowl = 6

Cup and Saucer = 8/2 = 4

Setting = 11 + 8 + 6 + 4 = $29

The change was 29-26.5 = $2.50

It seems like every dollar we add to the plate will add $2.50 to the cost of a setting.

So, if $11 for a plate gives us $29 a setting, we need to increase the cost by 44 – 29 = $15.  $15/2.5 = 6, so the price of a plate needs to be 6 higher than 11 or $17.

Check it

Try $17 for a dinner plate

Dinner plate = 17

Salad plate = 17-3 = 14

Soup bowl = 6

Cup and Saucer = 14/2 = 7

Setting = 17 + 14 + 6 + 7 = $44

Yes!