Two mechanics work on a car . The first mechanic worked 10 hours and the second mechanic worked for 15 hours. Together they charged a total of $2050. What was the rate charged by each mechanic if the sum of the two rates was $16 per hour?

and

Step-by-step explanation:

Let

x ----> the amount charged per hour by the first mechanic

y ----> the amount charged per hour by the second mechanic

we know that

the sum of the two rates was $16 per hour

so

----> equation A

Together they charged a total of $2050

so

----> equation B

solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (124,54)

see the attached figure

Find the rate charged by each mechanic

First mechanic

Second mechanic

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.