Explanation:
a. To determine if Taco Tom's claim that he could find possible combinations of tacos and tomatoes by using the equation 5x + 10y = 45, we can first rewrite the equation in terms of the number of tacos and tomatoes he can buy.
Assuming x represents the number of tomatoes and y represents the number of tacos, we can rewrite the equation as follows:
$$ 5x + 10y = 45 $$
Dividing both sides by 5, we get:
$$ x + 2y = 9 $$
This equation represents the relationship between the number of tomatoes and the number of tacos that Taco Tom can buy with his $45.
To check if Taco Tom's claim is correct, we can test various values of x and y that satisfy this equation. For example:
If Taco Tom buys 1 tomato and 4 tacos, then:
$$ x = 1, y = 4 $$
Substituting these values into the equation, we get:
$$ 5(1) + 10(4) = 45 $$
So, it is possible for Taco Tom to buy 1 tomato and 4 tacos with his $45.
Similarly, we can check other values of x and y that satisfy the equation and confirm that Taco Tom's claim is correct. Therefore, we agree with Taco Tom that there are possible combinations of tacos and tomatoes that he can buy with his $45 that satisfy the equation 5x + 10y = 45.