#5 antonio and abby had the same nimber of paperclips. after antonio gave 30 paperclips to abby, abby had twice as many paperclips as antonio. how many paperclips did they have in all?
#6 emily and jasmine had the same number of stamps. after emily gave 42 stamps to jasmine, jasmine had twice as many stamps as emily. how many stamps did jasmine have in the end?
#7 elena had 60 colored pencils. lucy had 26 colored pencils. how many pencils must elena give to lucy so that elena will have 4 more colored pencils than lucy?
show how you answered

#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, .

Let the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

Antonio gives paperclips to Abby. After that,

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.

Similarly, let be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

After Emily gives stamps to Jasmine:

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.

Let the number of pencils that Elena needs to give to Lucy be .

Initially:

After Elena gives pencils to Lucy:

Elena should now possess four more pencils than Lucy does. In other words,

.

.

.

df =

both have same length

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.