Question

13.) caleb, michael and steven went to james coney island for lunch. michael bought a drink, 2 hot dogs, and a basket of french fries and spent $10.50. steven spent $9.75 on a hot dog, 2 baskets of french fries, and a drink. caleb wasn’t very hungry, so he only bought a hot dog and a drink. caleb spent $6.25. let x = the cost of a hot dog, y = the cost of a basket of french fries, and z = the cost of a drink. write a system of equations to represent this situation.

14.) regal cinema sells student, adult, and senior citizen movie tickets. student tickets sell for $9.50, adult tickets are $12, and senior citizen tickets are $7.50. they sold a total of 2364 tickets last weekend and made a total of $18,260. the number of senior tickets sold was 12 less than twice the number of adult tickets sold. write a system of equations to represent this situation. be sure to define your variables.

15.) julie’s little brother, jacob, needed money. he asked julie if he could have the money she had saved in he piggy bank. julie told him that if he could figure out how many of each type of coin, she had that he could have th money. she gave him these clues: i have 20 less than dimes than quarters. the total amount of money is $20.55 there are 64 coins, and i only have dimes, nickels and quarters. write a system of equations to help jacob determine how many nickels, dimes, and quarters julie has.

Explanation:

Question 13

Step1: Analyze Michael's purchase

Michael bought a drink (\(z\)), 2 hot dogs (\(2x\)), and a basket of French fries (\(y\)) for \$10.50. So the equation is \(2x + y + z = 10.50\).

Step2: Analyze Steven's purchase

Steven bought a hot dog (\(x\)), 2 baskets of French fries (\(2y\)), and a drink (\(z\)) for \$9.75. So the equation is \(x + 2y + z = 9.75\).

Step3: Analyze Caleb's purchase

Caleb bought a hot dog (\(x\)) and a drink (\(z\)) for \$6.25. So the equation is \(x + z = 6.25\).

Step1: Define variables

Let \(s\) = number of student tickets, \(a\) = number of adult tickets, \(c\) = number of senior citizen tickets.

Step2: Total tickets sold

Total tickets sold is 2364, so \(s + a + c = 2364\).

Step3: Total money made

Student tickets: \$9.50 each, adult: \$12 each, senior: \$7.50 each. Total money is \$18,260, so \(9.50s + 12a + 7.50c = 18260\).

Step4: Relationship between senior and adult tickets

Senior tickets sold was 12 less than twice adult tickets, so \(c = 2a - 12\).

Step1: Define variables

Let \(n\) = number of nickels, \(d\) = number of dimes, \(q\) = number of quarters.

Step2: Total number of coins

Total coins: 64, so \(n + d + q = 64\).

Step3: Relationship between dimes and quarters

Dimes are 20 less than quarters: \(d = q - 20\).

Step4: Total amount of money

Nickels: \$0.05 each, dimes: \$0.10 each, quarters: \$0.25 each. Total money: \$20.55, so \(0.05n + 0.10d + 0.25q = 20.55\).

Answer:

The system of equations is:

$$
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$$

Question 14