Question

Two friends are planning for a gathering. the food budget is modeled by one half times the absolute value of the quantity x minus 120 end quantity equals 10 comma where x is the amount spent on food. what are the least and greatest amounts that the two friends could spend on food? $50, $70 $100, $140 $110, $130 $115, $125

Answer 1

The least amount is $100 and greatest amount is $140.

For given question,

We have been given the food budget is modeled by an equation,

1/2 |x - 120| = 10

where x is the amount spent on food.

We need to find the least and greatest amounts that the two friends could spend on food.

⇒ 1/2 |x - 120| = 10

⇒ |x - 120| = 20

We can observe that above equation contains absolute vale function.

⇒ x - 120 = ±20

⇒ x - 120 = -20         or          x - 120 = 20

⇒ x = 120 - 20          or          x = 120 + 20

⇒ x = 100               or         x = 140

Therefore, the least amount is $100 and greatest amount is $140.

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