Math

QuestionCody has \7tobuyatleast4snacks.Hotdogs7 to buy at least 4 snacks. Hot dogs (x)cost$2each,peanuts cost \$2 each, peanuts (y)$1each.Findvalid \$1 each. Find valid (x,y)pairs: pairs: x+y42x+y7 \begin{array}{r} x+y \geq 4 \\ 2x+y \leq 7 \end{array} Options: Options: (5,2),, (0,7)$

Studdy Solution

STEP 1

Assumptions1. Cody has 7.Hewantstobuyatleast4snacks3.Thecostofahotdog(x)is7. He wants to buy at least4 snacks3. The cost of a hot dog (x) is 4. The cost of peanuts (y) is $15. The ordered pairs are solutions to the system of inequalities

STEP 2

The first inequality represents the minimum number of snacks Cody wants to buy. The second inequality represents the maximum amount of money Cody can spend. We need to find an ordered pair (x, y) that satisfies both inequalities.
The first inequality isx+y4x + y \geq4The second inequality is2x+y72x + y \leq7

STEP 3

Let's check the first ordered pair (5,2). Substitute x=5 and y=2 into the inequalities.
For the first inequalityx+yx + y \geq5+25 +2 \geqFor the second inequality2x+y72x + y \leq725+272*5 +2 \leq7

STEP 4

Now, let's evaluate the inequalities.
For the first inequality+24 +2 \geq4747 \geq4For the second inequality2+272* +2 \leq712712 \leq7

STEP 5

The first inequality is true, but the second inequality is false. Therefore, the ordered pair (5,2) is not a solution to the system of inequalities.

STEP 6

Now, let's check the second ordered pair (0,). Substitute x=0 and y= into the inequalities.
For the first inequalityx+y4x + y \geq40+40 + \geq4For the second inequality2x+y2x + y \leq20+2*0 + \leq

STEP 7

Now, let's evaluate the inequalities.
For the first inequality0+740 +7 \geq4747 \geq4For the second inequality20+772*0 +7 \leq7777 \leq7

STEP 8

Both inequalities are true. Therefore, the ordered pair (0,7) is a solution to the system of inequalities.
So, Cody can buy0 hot dogs and7 peanuts.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord