Sandy sold half of her comic books and then bought 9 more. she now has 12. how many did she begin with write an equation and solve. me

Sandy began with a number of books that we don't know. Since that number is unknown to us, we use a variable to represent it. Let x = the number of books Sandy began with.

Sandy sold half of her comic books.

She sold x/2 books, and she kept x/2 books.

She kept x/2 books. Then she bought 9 books.

Now she has x/2 + 9 books. We are told she now has 12 books.

That means x/2 + 9 must equal 12. That gives us the equation.

Now we solve the equation. We subtract 9 from both sides.

Multiply both sides by 2.

Since we let x equal the number of books she began with, now we know she began with 6 books.

She began with 6 books.

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.