8. Joe can chop vegetables in 5 minutes, and Rich can chop the same amount of vegetables in 4 minutes. Working together, how long will it take them to chop that batch of vegetables? 9. At Ricardo's Tacos, four tacos and two orders of chips cost the same as two tacos and four orders of chips. If Ricardo's charges $2.00 for a single order of chips, how much does Ricardo's charge for 1 taco? 10. Broccoli is $1.69 per pound. Meg paid $8.45 for broccoli. How many pounds did she purchase?

Explanation:

8. Joe can chop vegetables in 5 minutes, and Rich can chop the same amount of vegetables in 4 minutes. Working together, how long will it take them to chop that batch of vegetables?

Name v the amount of vegetables

Working together, the combined speed is the sum of the two speeds: v/5 + v/4

Thus, the speed working together is:

Hence, they can chop 9 times the given amount of vegetables (v) in 20 minutes.

And the time to chop the given amount of vegetables (v) is 20 divided by 9.

That is 2.22 minutes to chop all the vegetables working together.

9. At Ricardo's Tacos, four tacos and two orders of chips cost the same as two tacos and four orders of chips. If Ricardo's charges $2.00 for a single order of chips, how much does Ricardo's charge for 1 taco?

Use T for the cost of tacos and C for the cost of orders of chips

Ricardo's charges the same for those orders:

Ricardo's charges $2.00 for a single order of chips:

Substitute C = 2 in 4T + 2C = 2T + 4C and solve:

   Substitution:

   Do the operations:

   Subtract 4 from both sides

   Subtract 2T from both sides

   Combine like terms

   Divide both sides by 2

Hence, Ricardo's charges $2.00 for one taco.

10. Broccoli is $1.69 per pound. Meg paid $8.45 for broccoli. How many pounds did she purchase?

You must divide the amount paid ($8.45) by the unit price ($1.69/lb)

In the operation, $ appears both in the numerator and the denominator so they cancel out each other. The unit pounds (lb) appears dividing the denominator, thus it passes to the numerator.

Hence, Meg purchased 5.00 pounds

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

faster, im not sure why but i know it is faster