Question

Lily has twice as many cards as Cameron. Sarah has three times as

many cards as Cameron. Pete has 10 fewer cards than Lily. Kyle
has 20 more cards than Pete. Kyle has 30 cards. How many cards
are in the game?

Answer 1

There are 100 cards in the game.

Explanation:

We can solve this problem using small equations and variables, where:

• T represents the total amount of cards in the game,
• L represents Lil's cards,
• C represents Cameron's cards,
• S represents Sarah's cards,
• P represents Pete's cards,
• and K represents Kyle's cards.

Step 1: Determine how many cards Pete has:

• We're told that Kyle has 30 cards.

Since Kyle has 20 more cards than Pete, we can determine how many cards Pete has using the following equation:

K = P + 20

(30 = P + 20) - 20

10 = P

Thus, Pete has 10 cards.

Step 2: Determine how many cards Lily has:

• We now know that Pete has 10 cards.

Since Pete has 10 fewer cards than Lily, we can determine how many cards Lily has using the following equation:

P = L - 10

(10 = L - 10) + 10

20 = L

Thus, Lily has 20 cards.

Step 3: Determine how many cards Cameron has:

• We now know that Lily has 20 cards.

Since Lily has twice as many cards as Cameron, we can determine how many cards Cameron has using the following equation:

L = 2C

(20 = 2C) / 2

C = 10

Thus, Cameron has 10 cards.

Step 4: Determine how many cards Sarah has:

• We now know that Cameron has 10 cards.

Since Sarah has three times as many cards as Cameron, we can determine how many cards Sarah has using the following equation:

S = 3C

S = 3(10)

S = 30

Thus, Sarah has 30 cards.

Step 5: Determine the total number of cards in the game:

Finally, we can determine the total number of cards in the game using the following equation:

T = L + C + S + P + K

T = 20 + 10 + 30 + 10 + 30

T = 100

Thus, there are 100 total cards in the game.

Answer 2

100 cards

Explanation:

Lily has twice as many cards as Cameron, so if Cameron has x cards, then Lily has 2x cards.

Sarah has three times as many cards as Cameron, so she has 3x cards.

Pete has 10 fewer cards than Lily, so he has 2x - 10 cards.

Kyle has 20 more cards than Pete, so he has 2x - 10 + 20 cards.

We know that Kyle has 30 cards, so we can set up the following equation:

2x - 10 + 20 = 30

Combining like terms, we get:

2x + 10 = 30

Subtracting 10 from both sides of the equation, we get:

2x = 20

Dividing both sides of the equation by 2, we get:

2x ÷ 2 = 20 ÷ 2

x = 10

So, Cameron has 10 cards, Lily has (2× 10) = 20 cards, Sarah has 3 × 10 = 30 cards, and Pete has (2 × 10 - 10 = 20 - 10) = 10 cards and Kyle has 30 cards.

In total, there are 10 + 20 + 30 + 10 + 30 = 100 cards in the game.