Multi step equations

Question

Ivan had 120 baseball cards. He gave some baseball cards to his brother, Nathan. Also, two-thirds of the number of cards given to Nathan was damaged and so, Ivan discarded them. If Ivan has 55 baseball cards now, how many cards did he give his brother?

Answer 1

Ivan had 120 baseball cards. He gave some baseball cards to his brother, Nathan. Also, two-thirds of the number of cards given to Nathan was damaged and so, Ivan discarded them. If Ivan has 55 baseball cards now, how many cards did he give his brother?

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Algebra is all about equations and working with unknowns.

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Think about the UNKNOWN in the problem above. The number of cards given to Nathan. Right?

In algebra, we assign a variable to that unknown value......like.....

let B be unknown number of cards given to Nathan (keep mind we can select any variable B, X, N....etc)

let D be unknown number of cards damaged.

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Now from the word problem description we translate the information into math equations using B and D.....like so...

2/3 (B) = D

120 - B - D = 55

.....120-B-2/3B = 55...

.....120 - 5/3 B = 55......

......65 = 5/3 B....multiply both sides of the equation by 3/5 to get....B=39.....here solved for B

---now solve for D-----

2/3 (39) = D = 26....

ALWAYS CHECK YOUR WORK AND VALUES AND MAKE SURE THEY ANSWER THE QUESTION....

.....check 120 - 39 - 26 = 55....that checks.....So he gave his brother 39 cards right?