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QuestionAlonso has \$21, buys eggs for \$2.50, and avocados cost \$5 per bag of 3.
1) Which inequality fits? (A) 2.50+5B≤212.50+5B \leq 21 (B) 2.50+5B≥212.50+5B \geq 21 (C) 2.50+3B≤212.50+3B \leq 21 (D) 2.50+3B≥212.50+3B \geq 21
2) What's the max number of avocados he can buy?

Studdy Solution

STEP 1

Assumptions1. Alonso has $21\$21 to spend. . The cost of eggs is $.50\$.50.
3. Avocados are sold in bags of3 for $5\$5.
4. Alonso wants to buy as many avocados as he can with his remaining money after buying eggs.
5. BB represents the number of bags of avocados that Alonso buys.

STEP 2

First, we need to set up an inequality to represent the scenario. The total amount Alonso spends on eggs and avocados must be less than or equal to the amount of money he has.Cost of eggs+Cost of avocados≤Total moneyCost\, of\, eggs + Cost\, of\, avocados \leq Total\, money

STEP 3

Now, plug in the given values for the cost of eggs, cost of avocados (which is 5B5B since each bag costs $5\$5), and total money to form the inequality.
$2.50+$5B≤$21\$2.50 + \$5B \leq \$21So, the correct answer for the first question is (A) 2.50+5B≤212.50+5 B \leq21.

STEP 4

To find the largest number of avocados Alonso can afford, we need to solve the inequality for BB.

STEP 5

Subtract $2.50\$2.50 from both sides of the inequality.
$5B≤$21−$2.50\$5B \leq \$21 - \$2.50

STEP 6

Calculate the right side of the inequality.
$5B≤$18.50\$5B \leq \$18.50

STEP 7

Divide both sides of the inequality by $5\$5 to solve for BB.
B≤$18.50/$5B \leq \$18.50 / \$5

STEP 8

Calculate the value of BB.
B≤3.7B \leq3.7Since Alonso can't buy a fraction of a bag, he can buy at most3 bags of avocados.

STEP 9

Since each bag contains3 avocados, multiply the number of bags by3 to find the total number of avocados Alonso can afford.
Number of avocados=3timesNumber of bagsNumber\, of\, avocados =3 \\times Number\, of\, bags

STEP 10

Plug in the value for the number of bags to calculate the number of avocados.
Number of avocados=3times3Number\, of\, avocados =3 \\times3

STEP 11

Calculate the number of avocados.
Number of avocados=3times3=9Number\, of\, avocados =3 \\times3 =9The largest number of avocados that Alonso can afford is9.

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