WORD PROBLEMS WITH EQUATIONS
-Harry and Nicky share $120 but Nicky takes $58 more than Harry. How much does each person have?
-When Katy was 12, her father was three times her age. Now he is twice her age. How old is Katy now?
-a rectangle is 4cm longer than it is wide. Its perimeter is 64cm. Find its dimensions.
-Mark has 28 10-cent and 20-cent pieces. How many of each coin does he have if their total value is $4.30?
-In a class of 26, there are four more boys than girls. How many boys are there?
THIS IS THE PART OF MY HOMEWORK THAT I DON'T UNDERSTAND. PLEASE KINDLY SHOW ME THE WORKING OUT. THANK YOU SO MUCH.
x + (x+58) = 120
Solve for x.
When Katy was 12, her father was 36 (3*12).
now 12 + x = 2(36+x)
Solve for x and add to Katy's age
2x + 2(x+4) = 64
I hope you can become aware of the process enough to do the remaining problems by yourself.
Sure! I'd be happy to help you understand how to solve these word problems with equations. Let's go through each one step by step.
1. Harry and Nicky share $120 but Nicky takes $58 more than Harry. How much does each person have?
Let's assume that Harry has x dollars. Since Nicky takes $58 more than Harry, we can say that Nicky has x + $58 dollars. The total amount they share is $120, so we can write the equation:
x + (x + $58) = $120
To solve this equation, we combine like terms and solve for x:
2x + $58 = $120
2x = $120 - $58
2x = $62
x = $31
So, Harry has $31 and Nicky has $31 + $58 = $89.
2. When Katy was 12, her father was three times her age. Now he is twice her age. How old is Katy now?
Let's assume Katy's current age is x. When she was 12, her father was three times her age, so we can write the equation:
12 + (x + father's age difference) = 3x
Now, we are told that her father is currently twice her age, so we can write the equation:
x + (x + father's age difference) = 2x
We have two equations, so let's solve them together:
12 + (x + father's age difference) = 3x
x + (x + father's age difference) = 2x
Simplify the equations:
12 + x + father's age difference = 3x
x + x + father's age difference = 2x
Combine like terms:
12 + 2x + father's age difference = 3x
2x + father's age difference = 2x
Subtract 2x from both sides:
12 + father's age difference = x
Since we are looking for Katy's current age, x represents her current age. Therefore, Katy is 12 years old now.
3. A rectangle is 4 cm longer than it is wide. Its perimeter is 64 cm. Find its dimensions.
Let's assume the width of the rectangle is x cm. Since the rectangle is 4 cm longer than it is wide, its length can be represented as x + 4 cm.
The perimeter of a rectangle is twice the sum of its length and width, so we can write the equation:
2(x + x + 4) = 64
Simplify the equation:
2(2x + 4) = 64
4x + 8 = 64
Subtract 8 from both sides:
4x = 64 - 8
4x = 56
Divide by 4:
x = 14
So, the width of the rectangle is 14 cm and the length is 14 + 4 = 18 cm.
4. Mark has 28 10-cent and 20-cent pieces. How many of each coin does he have if their total value is $4.30?
Let's assume Mark has x 10-cent coins. Since the total number of coins Mark has is 28, we can represent the number of 20-cent coins as (28 - x).
The total value of the 10-cent coins is 10x cents, and the total value of the 20-cent coins is 20(28 - x) cents. We are given that the total value is $4.30, which is equal to 430 cents. So we can write the equation:
10x + 20(28 - x) = 430
Simplify the equation:
10x + 560 - 20x = 430
Combine like terms:
560 - 10x = 430
Subtract 560 from both sides:
-10x = 430 - 560
-10x = -130
Divide by -10:
x = -130 / -10
x = 13
Since we can't have a negative number of coins, it means that Mark has 13 10-cent coins and (28 - 13) = 15 20-cent coins.
5. In a class of 26, there are four more boys than girls. How many boys are there?
Let's assume the number of girls in the class is x. Since there are four more boys than girls, we can represent the number of boys as (x + 4).
The total number of students in the class is 26, so we can write the equation:
x + (x + 4) = 26
Simplify the equation:
2x + 4 = 26
Subtract 4 from both sides:
2x = 26 - 4
2x = 22
Divide by 2:
x = 22 / 2
x = 11
So, there are 11 girls in the class. To find the number of boys, we substitute x back into the equation:
boys = x + 4 = 11 + 4 = 15
Therefore, there are 15 boys in the class.
I hope that helps! Let me know if you have any more questions.