Question

Rosa bought 1 pound of cashews and 2 pounds of peanuts for $10. At the same store, Sabrina bought 2 pounds of cashews and 1 pound of peanuts for $11. Find the cost per pound for cashews and peanuts.

Answer 1

(1)c + (2)p = 10 and (2)c + (1)p = 11

You now have 2 simultaneous equations in 2 variables that can be solved by either elimination or substitution. I would suggest elimination and you can do that by doubling equation #1 and subtracting that from equation #2. That will give you "p" for peanuts. Substitute that value into either equation to get "c".

Answer 2

c=$4 p=$3

Answer 3

Yes! Good job!

Answer 4

ok awesome thanks!

Answer 5

Mandy is skating at 5 miles per hour. Nikki is skating at 6 miles per hour and started 1 mile behind Mandy. If their rates stay the same, will Mandy catch up with Nikki? Explain.

I can't figure out the system for this

Answer 6

Nikki will eventually catch up because the relative speed of the 2 is 1 mile per hour (from 6 - 5). And since the initial gap is 1 mile, that gap will be closed in one hour.

Answer 7

thanks. What do you mean by "the relative speed of the 2"?

Answer 8

Setting this up as a system of equations looks like

distance = rate x time

d = 5 x t and d + 1 = 6 x t

You will see that d will equal 5 when t is 1.

And as for "the relative speed of the 2", the "2" means the 2 people.

Answer 9

ok. Got it.

Answer 10

One week Trey rented 4 DVDs and 2 video games for $18. The next week he rented 2 DVDs and 1 video game for $9. Find the rental costs for each video game and DVD. Explain your answer.

Just to check, dvds are $0 and video games are $9... correct?