### Brain Teasers

# Super Skateboards

Alec, Brett and Chris each purchased parts for their skateboards at the sports store. Alec and Brett wanted to build new skateboards, so they each needed to purchase a deck, trucks, bearings and wheels. Chris only needed new wheels. The store offers a 10% discount for purchases over $250, so the boys decided to pay for all the parts together to qualify for the discount. Altogether, the boys spent $266.40. The clues below reflect the price of the items before the discount is applied.

The cost of all the bearings for the 2 boys combined was $1 more than the deck for Alec's skateboard.

They each bought the same kinds of wheels. Together they spent $75 for the 3 sets of wheels. Each set contained 4 wheels.

The total cost of the bearings came to $24 less than the total cost of the wheels.

Alec spent $5 more for his deck than Brett spent for his. However, Brett spent $5 more on trucks than Alec.

Brett spent $3 more on bearings than twice the amount Alec spent on bearings.

How much did each person spend?

The cost of all the bearings for the 2 boys combined was $1 more than the deck for Alec's skateboard.

They each bought the same kinds of wheels. Together they spent $75 for the 3 sets of wheels. Each set contained 4 wheels.

The total cost of the bearings came to $24 less than the total cost of the wheels.

Alec spent $5 more for his deck than Brett spent for his. However, Brett spent $5 more on trucks than Alec.

Brett spent $3 more on bearings than twice the amount Alec spent on bearings.

How much did each person spend?

### Answer

Alec spent $113.40.

Brett spent $130.50.

Chris spent $22.50.

Component Alec Brett Chris Total

Deck $50 $45 $0 $95

Trucks 35 40 $0 75

Wheels 25 25 25 75

Bearings 16 35 $0 51

Total before discount $126 $145 $25 $296

less 10% discount $12.60 $14.50 $2.50 $29.60

Amount spent $113.40 $130.50 $22.50 $266.40

Explanation:

First find the original price of all the items combined. $266.40 is the price after the 10% discount was applied.

That means $266.40 is equal to 90% of the original price.

Write an equation and then cross multiply:

266.40

--------------------------------------------------------------------------------

x = 9

--------------------------------------------------------------------------------

x

The original price for all the items was $296.

Write an equation: (let the first letter of each word represent the total cost spent for that item).

D + T + W + B = 296

Given: The wheels cost $75.

D + T + W + B = 296

D + T -75 + B = 296 - 75

D + T + B = 221

The total cost of the bearings came to $24 less than the total cost of the wheels.

B = W - 24

B = 75 - 24

B = 51

The cost of all the bearings for the 2 boys combined was $1 more than the deck for Alec's skateboard.

Alec's skateboard = 51 - 1

Alec's skateboard = 50

Alec spent $5 more for his deck than Brett spent for his.

Alec spent $50. Therefore, $50 - 5 = Brett's deck

Brett's deck = $45.

However, Brett spent $5 more on trucks than Alec.

Add the amounts known on all of the items so far and subtract from the total original cost.

Wheels: 75

Decks: 95

Bearings: 51

75 + 95 + 51 = 221

Sub total: 221

Therefore, the total amount spent on trucks was $75.

Total amount on trucks was $75. To find the amount each boy spent: use a formula or guess and check (What 2 numbers total 75, if one is 5 more than the other?)

Let x = the amount Alec spent on trucks.

x + (x+5) = 75

2x + 5 = 75

2x = 70

x = 35

Alec spent $35 on trucks. Brett spent $5 more than Alec. Therefore, Brett spent $40 on trucks.

Brett spent $3 more than twice the amount Alec spent on bearings.

Here, let x = the amount Alec spent on bearings.

Brett spent $3 more than twice the amount Alec spent on bearings, so write the value of Brett's bearings as 2x + 3.

Amount Alec spent + amount Brett spent = $51

x + (2x + 3) = 51

3x + 3 = 51

3x = 48

x = 16

Alec's spent $16 on bearings.

Brett spent $35 on bearings

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