Question

Tanya bought 3 games on her phone that each cost the same amount. Tony

bought 4 games on his phone that each cost the same amount, but each was
$.50 less than the games that Tanya bought. Both Tanya and Tony paid the
same amount of money. What was the cost of one of Tanya’s games?

(a) Write an expression that shows Tanya’s purchased games.
• Hint-Let x represent the cost of one of Tanya's items.
(b) Write an expression that show Tony’s purchased games.
• Hint-Let x represent the cost of one of Tanya's items.

(c) Write an equation that you can solve to see the cost of each person’s
games. Let x represent the cost of one of Tanya's games.

• Hint- Tanya and Tony paid the same amount.
(d) Solve the equation. Show your work.

Answer 1

Explanation:

a) Let x be the price of one of Tanya's games and y be the price of one of Tony's games. We know that Tony's games cost 0.50 less than Tanya's then

y = x-0.5

Tanya bought 3 games, so the amount of games she purchased is 3*x.

b) On the same fashion, Tony bought 4 games. So the amount he purchased is 4*y = 4*(x-0.5).

c) Since both spent the same money, we have that 3*x = 4*(x-0.5)

ON the right hand side, distribute the multiplication, so you get

3x = 4x- 4*0.5 = 4x-2.

Then, substract 3x on both sides

3x-3x = 0 = 4x-3x-2 = x-2

Then, add 2 on both sides

0+2 = 2 = x-2+2 = x .

This means, that Tanya's games cost 2 each and Tony's games cost 1.50 each.

Note that 2*3 = 6 = 4*1.50, which proves that x=2 is the correct answer.

Answer 2

Let the price of a game be X

Tonya bought three so you have 3X

Tony 's games were 0.50 less, so his price was x-0.50.

He bought 4 games so you have 4(X-0.50)

Now set the two equations to equal each other because they paid the same total amount:

3x = 4(x-0.50)

Now solve:

3x = 4(x-0.50)

Use distributive property:

3x = 4x - 2

Subtract 4x from both sides:

-x = -2

Divide both sides by -1:

x = 2

The price Tonya paid per game was $2

$2 x 3 games = $6 total.

The price Tony paid per game was $1.50

$1.50 x 4 games = $6 total.