Question

Harrison and pia buy x comic books for $5.00 each Harrison also buys an action figure for $15 while pia buys a different action figure for $12 could they each spend the same amount y and the same number comic books.explain

Answer 1

Answer:

no

yes

Step-by-step explanation:

they each buy x comic books for $5 each.

we don't know the total number of comic books they bought, but we know they bought the same number (x). and because each comic book had the same price ($5), we know they even spent the same amount of money on comic books (5x).

so, yes, they bought the same number of comic books.

but now, Harrison bought an action figure for $15, and Pia bought one for $12.

so, Harrison spent y = x + $15, and Pia spent y = x + $12.

as x has the same value in both cases, the sum y cannot be the same, because 15 is not equal to 12.

so, no, they could not spend the same amount.

Answer 2

Answer:

No, Harrison and Pia cannot each spend the same amount and buy the same number of comic books since the action figures they each purchase have different costs.

Step-by-step explanation:

Let x be the number of comic books each person buys.

Let y be the total amount each person spends.

Since each comic book costs $5.00, the cost of x comic books for both Harrison and Pia would be 5x.

Harrison also buys an action figure for $15.00. So, the total amount he spends is represented by the equation:

$y = 5x + 15$

Pia also buys an action figure for $12.00. So, the total amount she spends is represented by the equation:

$y = 5x+12$

To determine if they could each spend the same amount (y) and buy the same number of comic books (x), we can set up an equation:

$5x + 15 = 5x + 12$

To simplify, subtract 5x from both sides of the equation:

$15 = 12$

This statement is not true and is a contradiction. This implies that the cost of the comic books and action figures cannot be equal for both Harrison and Pia. Therefore, they cannot each spend the same amount (y) and buy the same number of comic books (x).