Question

Abigail and her children went into a movie theater and she bought $71.50 worth of drinks and pretzels. Each drink costs $4 and each pretzel costs $4.75. She bought a total of 16 drinks and pretzels altogether. Determine the number of drinks and the number of pretzels that Abigail bought.

Answer 1

The number of drinks is 6 and the number of pretzels is 10 that Abigail bought

Step-by-step explanation:

Abigail and her children went into a movie theater

• She bought $71.50 worth of drinks and pretzels
• Each drink costs $4 and each pretzel costs $4.75
• She bought a total of 16 drinks and pretzels altogether

We need to find the number of drinks and the number of pretzels that Abigail bought

Assume that she bought x drinks and y pretzels

∵ x represents the number of drinks

∵ y represents the number of pretzels

∵ Each drink costs $4

∵ Each pretzel costs $4.75

∵ she payed $71.50

- Multiply x by 4 and y by 4.75, then add the products and

   equate the sum by 71.50

∴ 4x + 4.75y = 71.50 ⇒ (1)

∵ She bought a total of 16 drinks and pretzels altogether

- Add x and y, then equate the sum by 16

∴ x + y = 16 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (2) by -4 to eliminate x

∵ -4 x - 4y = -64 ⇒ (3)

- Add equations (1) and (3)

∴ 0.75y = 7.5

- Divide both sides by 0.75

∴ y = 10

- Substitute the value of y in equation (2) to find x

∵ x + 10 = 16

- Subtract 10 from both sides

∴ x = 6

The number of drinks is 6 and the number of pretzels is 10 that Abigail bought

Learn more:

You can learn more about the system of equations in brainly.com/question/3739260

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