Answer:
#5: 180 paperclips in total.
#6: 126 stamps in total.
#7: Elena should give Lucy 15 colored pencils.
Step-by-step explanation:
This explanation solves each question by setting a single unknown, .
<h3>#5</h3>
Let the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.
Initially:
- Antonio: paperclips;
- Abby: paperclips.
Antonio gives paperclips to Abby. After that,
- Antonio: paperclips;
- Abby: paperclips.
Abby now possess twice as many paperclips as Antonio does. In other words,
.
By the distributive property:
.
Substract from both sides
.
Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.
<h3>#6</h3>
Similarly, let be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.
Initially:
- Emily: stamps;
- Jasmine: stamps.
After Emily gives stamps to Jasmine:
- Emily: stamps;
- Jasmine: stamps.
Jasmine now possesses twice as many stamps as Emily does. In other words,
.
.
Jasmine used to possess 126 stamps. Now she possesses stamps after receiving stamps from Emily.
<h3>#7</h3>
Let the number of pencils that Elena needs to give to Lucy be .
Initially:
- Elena: 60 pencils;
- Lucy: 26 pencils.
After Elena gives pencils to Lucy:
- Elena: pencils;
- Lucy: pencils.
Elena should now possess four more pencils than Lucy does. In other words,
.
.
.