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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