Write and solve each equation from the given word problem on a blank sheet of paper. Write your answers in a complete sentence on this page. Show Your Work
1.) Maria combines her 39 seashells with Jacob’s seashells for a total of 173 seashells. Find how many seashells Jacob had before the collections were combined.
2.) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
3.) An emergency plumber charges $65 as a call-out fee plus an additional $75 per hour. He arrives at a house at 9:30 and works to repair a water tank. If the total repair bill is $196.25, at what time was the repair completed?
4.) To convert temperatures in Fahrenheit to temperatures in Celsius, take the temperature in degrees Fahrenheit, subtract 32, and then divide the result by 1.8. This gives the temperature in degrees Celsius. Write an equation that shows the conversion process.
4a.) Convert 50 degrees Fahrenheit to degrees Celsius.
4b.) Convert 25 degrees Celsius to degrees Fahrenheit.
5.) Jasmin’s dad, Andrew, is planning a surprise birthday party for her. He will hire a bouncy castle, and will provide party food for all the guests. The bouncy castle costs $150 for the afternoon, and the food will cost $3 per person. Andrew has a budget of $300. Write an equation and use it to determine the maximum number of guests he can invite.
6.) The speed of a body is the distance it travels per unit of time. That means that we can also find out how far an object moves in a certain amount of time if we know its speed: we use the equation “distance = time x speed” Shanice’s car is traveling 10 miles per hour slower than twice the speed of Brandon’s car. She covers 93 miles in 1 hour 30 minutes. How fast is Brandon driving?
7.) The electrical current, I (amps), passing through an electronic component varies directly with the applied voltage, V (volts), according to the relationship V=I⋅R where R is the resistance measured in Ohms (Ω).
a. A scientist is trying to deduce the resistance of an unknown component. He labels the resistance of the unknown component x Ω. The resistance of a circuit containing a number of these components is (5x+20) Ω. If a 120 volt potential difference across the circuit produces a current of 2.5 amps, calculate the resistance of the unknown component.
8.) A factory manager is packing engine components into wooden crates to be shipped on a small truck. The truck is designed to hold sixteen crates, and will safely carry a 1200 lb cargo. Each crate weighs 12 lbs empty. How much weight should the manager instruct the workers to put in each crate in order to get the shipment weight as close as possible to 1200 lbs?
9.) The lifespan of a guinea pig is 6 years less than that of a giraffe. The lifespan of a tiger is 4 times that of the guinea pig. If the total lifespan of the animals is 30 years, calculate the longevity for the giraffe.
10.) Danielle baked macaroni for her children for which she used up 1/9 th of a jug of milk. She also poured 20.5 ounces of milk into a bowl of cornflakes. If 25.5 ounces of milk remain in the jug, how much milk did the jug originally contain?
11.) Katrina’s uncle loaned her $1200 to buy a computer. Katrina plans to pay her uncle $75 per month until the loan is paid off. How many months will it take Katrina to pay back the money?
12.) A medical center is planning to hire a total of 54 nurses and CNAs (Certified Nursing Assistants). If the center needs twice as many CNAs as nurses, how many of each should they hire?
13.) A company is ordering 350 t-shirts to sell at a fundraiser. The company wants to order the same number of large size t-shirts as medium size t-shirts, but only half as many small t-shirts. How many of each size should they order?
14.) The perimeter of the triangle shown to the right is 26 inches. Determine the length of each side of the triangle. The three sides of triangle lenght are 3x, x, and 2x+8
