The least and greatest amounts that the two friends could spend on food would be 114 and 146.
We have,
The food budget is modeled by an equation,
i.e.
|x - 130| = 8
Here,
x = the amount spent on food
So,
Now,
According to the question,
To find the least and greatest amounts that the two friends could spend on food,
We have to,
Find absolute value of the quantity x,
i.e.
|x - 130| = 8
We get,
|x - 130| = 16
i.e.
x - 130 = ± 16
So,
The least amount will be, when we take negative value,
i.e.
x - 130 = - 16
On solving we get,
x = 114,
NOw,
The greatest amount will be, when we take positive value,
i.e.
x - 130 = 16
On solving we get,
x = 146,
So,
The least amount is 114 and greatest amount is 146.
Hence we can say that the least and greatest amounts that the two friends could spend on food would be 114 and 146.
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