Two friends are planning for a gathering. the food budget is modeled by one half times the absolute value of the quantity x minus

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?

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  1. An absolute value of |x| {modulus of x} is the value of a real number x. The least and greatest amounts that the two friends could spend on food are 100 and 140, respectively.

    What is Absolute Value?

    An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
    Given that the food budget is modeled as (1/2)|x – 120|=10, where x is the amount spent on food.
    Since in the given equation for the absolute quantity the critical point is 120. Therefore, we can write,
    A.) When the value of x≥120,
    (1/2)|x – 120|=10
    |x – 120| = 10 × 2
    |x – 120| = 20
    Now, the value of x is greater than 120, the absolute quantity will be positive,
    x – 120 = 20
    x = 20 + 120
    x = 140
    B.) When the value of x<120,
    (1/2)|x – 120|=10
    |x – 120| = 10 × 2
    |x – 120| = 20
    Now, the value of x is less than 120, the absolute quantity will be negative,
    -(x – 120) = 20
    -x + 120 = 20
    -x = 20 – 120
    -x = -100
    x = 100
    Hence, the least and greatest amounts that the two friends could spend on food are 100 and 140, respectively.
    Learn more about Absolute value here:
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