Thread: Math Word Problems

My math homework's due tomorrow, and I've been trying to solve these questions for a while now but I just keep getting the wrong answer / different answers each time, compared to the answers in the back of the book. So if someone could explain to me how to solve these problems step by step, that would be greatly appreciated!

"What mass of peanuts should be added to 1 kg of cashews so that the mixture is 75% peanut, by mass?"


"Maya puts $1.75 in nickels, dimes and quarters into a vending machine. The number of quarters she used was one more than the number of nickels. The number of dimes was one less than the number of nickels. How many of each type of coin did she use?"


"The two biggest lakes in Manitoba are Lake Winnipeg and Lake Winnipegosis. Their combined area is 29 800 km squared. The area of Lake Winnipegosis is 700 km squared less than one quarter of the area of Lake Winnipeg. What is the area of each lake?"


Again, it'd be great if someone could show me the steps on how to solve these word problems.

"What mass of peanuts should be added to 1 kg of cashews so that the mixture is 75% peanut, by mass?"

peanut is 1005% peanut
cashew is 0% peanut

Let P = mass pf peanuts to be added

P(100%) +1kg(0%) = (P +1kg)(75%)
100P +0 = 75(P +1kg)
100P -75P = 75kg
25P = 75kg
P = 75/25 = 3 kg of peanuts ------answer.

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"Maya puts $1.75 in nickels, dimes and quarters into a vending machine. The number of quarters she used was one more than the number of nickels. The number of dimes was one less than the number of nickels. How many of each type of coin did she use?"

(0.5)N +(0.10)D +(0.25)Q = 1.75 -------(1)
Q = N +1 -------(2)
D = N -1 ------(3)

Solve the 3 equations simultaneously to get
N = 4 nickels
D = 3 dimes
Q = 5 quarters

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"The two biggest lakes in Manitoba are Lake Winnipeg and Lake Winnipegosis. Their combined area is 29 800 km squared. The area of Lake Winnipegosis is 700 km squared less than one quarter of the area of Lake Winnipeg. What is the area of each lake?"

Wg +Ws = 29,800 -------(i)
Ws = (1/4)Wg - 700 ------(ii)

Solve the two equations simultaneously to get
Wg = 24,400 sq.km.
Ws = 5,400 sq.km.