Amedical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. if the average bill for a patient is between $200 and $800, find the range of the original bill.

It is stated that the total bill the patient would only pay would be the $25 plus 20% of the original bill. Therefore this would mean that:

25 + 0.2 * X = 200         ---> 1

25 + 0.2 * X = 800         ---> 2

Where X represents the original bill.

Calculating for X in equation 1:

25 + 0.2 * X = 200

0.2 * X = 175

X = 875

Calculating for X in equation 2:

25 + 0.2 * X = 800

0.2 * X = 775

X = 3875

Therefore the original bill ranges from $875 to $3875. The equality equation would be:

$875 ≥ X ≥ $3875

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.