Math  /  Algebra

QuestionJimmy receives his first 3 video games free then pays $50\$ 50 for each game after that.
Is the amount of money he spends on video games proportional to the number of games he owns?
Choose 1 answer: (A) Yes (B) No

Studdy Solution

STEP 1

What is this asking? Does the total cost of Jimmy's video games increase at a constant rate as he gets more games? Watch out! Don't get tricked by the initial free games!
Proportionality is all about a constant relationship *after* the starting point.

STEP 2

1. Check the Cost for a Few Games
2. Compare the Ratios

STEP 3

Let's see how much Jimmy spends as he gets more games.
This will help us see the pattern!

STEP 4

For the first **3 games**, Jimmy pays $0\$0.
That's right, absolutely **free**!
So, for 3 games, the cost is $0\$0.

STEP 5

For the 4th game, Jimmy pays $50\$50.
So, for **4 games**, the total cost is $0+$50=$50 \$0 + \$50 = \$50 .

STEP 6

For the 5th game, Jimmy pays another $50\$50.
So, for **5 games**, the total cost is $50+$50=$100 \$50 + \$50 = \$100 .

STEP 7

Let's do one more!
For the 6th game, another $50\$50.
So, for **6 games**, the total cost is $100+$50=$150 \$100 + \$50 = \$150 .

STEP 8

Now, let's see if the relationship between the number of games and the total cost is proportional.
We can do this by comparing the ratios of cost to games.

STEP 9

For **3 games** costing $0\$0, the ratio is $03=$0\frac{\$0}{3} = \$0 per game.

STEP 10

For **4 games** costing $50\$50, the ratio is $504=$12.50\frac{\$50}{4} = \$12.50 per game.

STEP 11

For **5 games** costing $100\$100, the ratio is $1005=$20\frac{\$100}{5} = \$20 per game.

STEP 12

For **6 games** costing $150\$150, the ratio is $1506=$25\frac{\$150}{6} = \$25 per game.

STEP 13

Whoa, hold on!
These ratios ($0 \$0 , $12.50\$12.50 , $20\$20 , $25\$25 ) are all different!
If the relationship were proportional, the ratio would be the same for every number of games.

STEP 14

The cost is *not* proportional to the number of games.
So the answer is (B) No.

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