Question

Write the equations: The difference of two numbers is 3 and their sum is 13. What are the two numbers?

Answer 1

Write the equations: The difference of two numbers is -10 and the sum is -4.

Answer 2

Write the equations: Two of Julie’s textbooks are a total of $65. The difference in price between the two books is $9. What is the cost of each book?

Answer 3

Write the equations: Jack and his sister Malonie are 4 years apart in age. The sum of their ages is 28. What are their ages?

Answer 4

Let's call the two numbers x and y. The difference of two numbers is 3 can be represented as:

x - y = 3 (Equation 1)

Their sum is 13 can be represented as:

x + y = 13 (Equation 2)

Now we can solve this system of equations to find the values of x and y.

Adding Equation 1 and Equation 2, we get:

(x - y) + (x + y) = 3 + 13

2x = 16

Dividing both sides by 2, we get:

x = 8

Substituting the value of x back into Equation 2:

8 + y = 13

Subtracting 8 from both sides, we get:

y = 13 - 8

y = 5

Therefore, the two numbers are 8 and 5.

Answer 5

Let's call the two numbers x and y.

The difference of two numbers is -10 can be represented as:

x - y = -10 (Equation 1)

The sum of the two numbers is -4 can be represented as:

x + y = -4 (Equation 2)

Now we can solve this system of equations to find the values of x and y.

Adding Equation 1 and Equation 2, we get:

(x - y) + (x + y) = -10 + (-4)

2x = -14

Dividing both sides by 2, we get:

x = -7

Substituting the value of x back into Equation 2:

-7 + y = -4

Adding 7 to both sides, we get:

y = -4 + 7

y = 3

Therefore, the two numbers are -7 and 3.

Answer 6

Let's call the cost of one textbook x and the cost of the other textbook y.

We are given two conditions:

1) The total cost of the two textbooks is $65. This can be represented as:

x + y = 65 (Equation 1)

2) The difference in price between the two books is $9. This can be represented as:

|x - y| = 9 (Equation 2)

Since we are only interested in the difference in price, we can use the absolute value to eliminate the possibility of negative differences.

Now we have a system of two equations. To solve for the cost of each book, we can solve this system of equations.

From Equation 2, we have two possibilities:

1) x - y = 9 (since the cost of the first book is greater than the cost of the second book)
2) y - x = 9 (since the cost of the second book is greater than the cost of the first book)

Let's solve both cases:

Case 1: x - y = 9

Adding this equation to Equation 1, we get:

(x + y) + (x - y) = 65 + 9

Simplifying this equation gives us:

2x = 74

Dividing both sides by 2, we find:

x = 37

Substituting this value back into Equation 1, we get:

37 + y = 65

Subtracting 37 from both sides, we find:

y = 28

So, the cost of the first book is $37 and the cost of the second book is $28.

Case 2: y - x = 9

Adding this equation to Equation 1, we get:

(x + y) + (y - x) = 65 + 9

This simplifies to:

2y = 74

Dividing both sides by 2, we find:

y = 37

Substituting this value back into Equation 1, we get:

x + 37 = 65

Subtracting 37 from both sides, we find:

x = 28

So, the cost of the first book is $28 and the cost of the second book is $37.

In conclusion, the cost of the first book can be either $37 or $28, and the cost of the second book will be the difference, $28 or $37 respectively.

Answer 7

Let's call Jack's age x and Malonie's age y.

According to the problem, Jack and Malonie are 4 years apart in age. This can be represented as:

x - y = 4 (Equation 1)

The sum of their ages is 28. This can be represented as:

x + y = 28 (Equation 2)

Now we have a system of two equations. To solve for their ages, we can solve this system of equations.

We can solve for x by adding Equation 1 and Equation 2:

(x - y) + (x + y) = 4 + 28

Simplifying this equation gives us:

2x = 32

Dividing both sides by 2, we find:

x = 16

Substituting this value back into Equation 2:

16 + y = 28

Subtracting 16 from both sides, we find:

y = 12

Therefore, Jack is 16 years old and Malonie is 12 years old.