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Elizabeth and her children went into a movie theater where they sell bags of popcorn for $\$7.50$ each and pretzels for $\$4.50$ each. Elizabeth has $\$120$ to spend and must buy at least $18$ bags of popcorn and pretzels altogether. If Elizabeth decided to buy $7$ bags of popcorn, determine all possible values for the number of pretzels that she could buy.

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GCF and LCM: word problems

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Q. Elizabeth and her children went into a movie theater where they sell bags of popcorn for

\$7.50

each and pretzels for

\$4.50

each. Elizabeth has

\$120

to spend and must buy at least

18

bags of popcorn and pretzels altogether. If Elizabeth decided to buy

7

bags of popcorn, determine all possible values for the number of pretzels that she could buy.

Calculate Popcorn Cost: question_prompt: How many pretzels can Elizabeth buy if she buys $7$ bags of popcorn and has $\$120$ to spend, given that she needs to buy at least $18$ items in total?
Calculate Remaining Budget: Calculate the total cost for $7$ bags of popcorn. $7$ bags $\times$ $\$7.50$ per bag = $\$52.50$ .
Calculate Pretzels Quantity: Subtract the cost of the popcorn from the total budget to find out how much money is left for pretzels. $\$120 - \$52.50 = \$67.50$ .
Check Total Items Requirement: Calculate the maximum number of pretzels Elizabeth can buy with the remaining money. $\$67.50 / \$4.50$ per pretzel = $15$ pretzels.
Determine Possible Pretzels Range: Check if buying $7$ bags of popcorn and $15$ pretzels meets the requirement of buying at least $18$ items. $7 + 15 = 22$ items, which is more than $18$ .
Determine Possible Pretzels Range: Check if buying $7$ bags of popcorn and $15$ pretzels meets the requirement of buying at least $18$ items. $7 + 15 = 22$ items, which is more than $18$ . Since Elizabeth can buy up to $15$ pretzels and needs to buy at least $18$ items in total, the possible values for the number of pretzels are from $11$ to $15$ . This is because she already has $7$ bags of popcorn, so she needs at least $11$ more items to reach $18$ .

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