BIG IDEAS MATH -

Question

The table shows the amounts of food collected by two homerooms. Homeroom A collects 21 additional items of food. How many more items does Homeroom B need to collect to have more items per student?

Homeroom AHomeroom B
Students	$24$24​	$16$16​
Canned Food	$30$30​	$22$22​
Dry Food	$42$42​	$24$24​

 

Homeroom B needs to collect more items.

Answer 1

72/24 = 3

(72+21)/(24) = 93/24

((22+24)+x)/16 = (46+x)/16

(46+x)/16 = 93/24

24(46+x) = 93(16)

24x = 93(16)- 24(46)

x = 93(16)/24 - 24(46)/24)

x = 93(2)/3 -46= 62-46 = 16 more makes them equal

17 more items will make B have a greater item to student ratio than homeroom A

(46+16)/16 = (72+21)/24

62/16 =93/24

31/16 = 31/8