Deanna Jones opened a video rental store this year with 400 tapes. She plans to buy 150 new tapes each year from now on. Deanna expects to have 1300 tapes available during her fifth year in business. At her current purchasing rate, will she reach her goal? Explain.

No, Deanna will not reach her goal.

Step-by-step explanation:

Let t represent number of years.  

We have been given Deanna Jones opened a video rental store this year with 400 tapes. She plans to buy 150 new tapes each year from now on.

We can see that the number of tapes bought by Deanna forms an arithmetic sequence, where 1st term is 400 and common difference is 150.

a = First terms,

n = Number of terms,

d = Common difference.

Upon substituting our given values, we will get:

To find the number of tapes that Deanna will have in 5th year, we will substitute in our formula.

Since Deanna will have 1000 tapes in 5th year which is less than 1300, therefore, she will not reach 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.