Kate has a summer job as a swim instructor to earn her college tuition. She gets paid $4 per hour for the first 30 hours and $6 per hour for each hour in the week worked over 30 hours. Kate's goal is to earn at least $144 per week. How many hours of overtime per week will she need to achieve her goal?

4 hours.

Step-by-step explanation:

According to the statement, you know that the amount she earns per week is equal to the first 30 hours for the price per hour that is $4 plus the number of hours over 30 hours multiply for its price that is $6. According to this, you can write the following equation where x is the hours of overtime per week:

4(30)+6x=144

120+6x=144

Now, you can solve for x:

6x=144-120

6x=24

x=24/6

x= 4

According to this, the answer is that Kate will need 4 hours of ovetime per week to achieve her goal.

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.