Question

Jackson has a gift card for $120 to use at a department store. He wants to purchase 2 shirts and 3 pairs of pants with his gift card. If x represents the cost of the shirts and y represents the cost of the pants, what are the domain and range of this relationship? A. domain: 0 ≤ x ≤ 60 range: 0 ≤ y ≤ 40 B. domain: 0 ≤ x ≤ 40 range: 0 ≤ y ≤ 60 C. domain: x ≥ 0 range: y ≥ 0 D. domain: 0 ≤ x ≤ 120

Answer 1

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Answer 2

The correct answer is option (A). domain: 0 ≤ x ≤ 60 and range: 0 ≤ y ≤ 40.

Given:

The amount in offered in the gift card = $120.

The number of shirts to be purchased by Jackson = 2.

The number of pants to be purchased by Jackson = 3.

The terms "x" and "y" represents the cost of the shirts and pants, respectively.

To Find:

We have to find the domain and range of the given relationship.

Solution:

Given that "x" and "y" represents the cost of the shirts and pants, respectively.

Therefore, a relation connecting the total amount and the number of shirts and pants to be purchased can be made into an equation as follows.

$2x + 3y \leq 120$.

If all the money is spent on purchasing 2 shirts, the equation for the price of the shirt is given by,

$0\leq 2x \leq 120$.

This can be simplified as, $0\leq x \leq 60$.

This equation forms the domain of the given relationship.

Similarly, if all the money is spent on purchasing 3 pants, the equation for the price of the pants is given by,

$0\leq 3x \leq 120$.

This can be simplified as, $0\leq x \leq 40$.

This equation forms the range of the given relationship.

Hence, the domain and range of the given relationship is 0 ≤ x ≤ 60 and 0 ≤ y ≤ 40, respectively.

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