Grades 7-8 Video Solutions 2021-video 2021 7-8/12

Video Transcription

Question 12. A jar one-fifth filled with water weighs 560 grams. The same jar four-fifths filled with water weighs 740 grams. What is the weight of the empty jar?  To do this, we can make some formulas. We know that one jar plus one-fifth of water is equal to 560 grams, and that one jar with four-fifths of water is equal to 740 grams.  We know that the jar plus one-fifth of water is 180 grams less than the jug plus four-fifths of water, so we can make a formula reflecting this.  A jar plus four-fifths of water is equal to a jar plus one-fifth of water plus 180 grams.  If we subtract out the jar from both sides, we get four-fifths of water is equal to one-fifth of water plus 180 grams.  We can subtract the one-fifth of water and get three-fifths of water is equal to 180 grams. If we divide both sides by three, one-fifth of water is equal to 60 grams.  If we take a look at our original formula of a jar of water plus one-fifth water is equal to 560 grams, then we can substitute one-fifth water for 60 grams and get a jar plus 60 grams is equal to 560 grams.  If we subtract 60 grams from both sides, then we get a jar is 500 grams. That is our answer, E, 500 grams.

Video Summary

The problem involves determining the weight of an empty jar based on given data: a jar one-fifth filled with water weighs 560 grams, and the same jar four-fifths filled weighs 740 grams. By establishing equations and solving them, it is determined that three-fifths of the water weighs 180 grams, indicating one-fifth is 60 grams. Substituting this information back into the equation for the jar one-fifth filled with water reveals the empty jar weighs 500 grams. Thus, the weight of the empty jar is 500 grams.

Keywords

empty jar weight

water weight calculation

equation solving

jar measurement

mathematical problem