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

1. bonexptip
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.