what is the equations "The sum of two numbers is 75. The first is 9 more than 5 times the second. Find the first number?"

What is the equations "Jack's bowling score is 20 less than 3 times Jill's score. Thw sum of their scores is 220. Find the score of each?"

a + b = 75

a = 5b+9
or,
a + b = 75
a - 5b = 9
so,
6b = 66
b=11 a=64
___________________

jack = 3*jill - 20
jack + jill = 220
or,
jack - 3jill = -20
jack + jill = 220
so,
4jill = 240
jill = 60 jack = 160

Oh, equations, you sly little things. Let's tackle them one by one, shall we?

For the first equation, let's call the first number "x" and the second number "y." We're given two pieces of information: (1) the sum of the two numbers is 75, and (2) the first number is 9 more than 5 times the second. So we can set up two equations:

Equation 1: x + y = 75
Equation 2: x = 5y + 9

Now, we have a system of equations. To solve it, we can substitute Equation 2 into Equation 1:

(5y + 9) + y = 75

Solving for y, we find that y = 12. Now, plug this value of y back into Equation 2 to find x:

x = 5(12) + 9

Evaluating that, we get x = 69. So the first number is 69.

Moving on to the second equation, let's say Jack's score is "a" and Jill's score is "b." We know two things: (1) Jack's score is 20 less than 3 times Jill's score, and (2) the sum of their scores is 220. So we can set up two equations:

Equation 1: a = 3b - 20
Equation 2: a + b = 220

To make things simpler, let's substitute Equation 1 into Equation 2:

(3b - 20) + b = 220

Simplifying, we find that 4b - 20 = 220. Solving for b, we get b = 60. Now, plug this value of b back into Equation 1 to find a:

a = 3(60) - 20

Doing the math, we get a = 160. So Jack's score is 160 and Jill's score is 60.

Sure! Let's solve the equations step-by-step:

Equation 1:
"The sum of two numbers is 75. The first is 9 more than 5 times the second."

Let's assume the second number as 'x'.
So, the first number would be 5x + 9.

According to the equation, their sum is 75:
x + (5x + 9) = 75.

Simplifying the equation:
6x + 9 = 75.

Subtracting 9 from both sides:
6x = 66.

Dividing both sides by 6:
x = 11.

So, the second number is 11.

To find the first number, we substitute the value of x back into the equation:
First number = 5x + 9 = 5(11) + 9 = 55 + 9 = 64.

Therefore, the first number is 64.

Equation 2:
"Jack's bowling score is 20 less than 3 times Jill's score. The sum of their scores is 220."

Let's assume Jill's score as 'x'.
So, Jack's score would be 3x - 20.

According to the equation, their sum is 220:
x + (3x - 20) = 220.

Simplifying the equation:
4x - 20 = 220.

Adding 20 to both sides:
4x = 240.

Dividing both sides by 4:
x = 60.

So, Jill's score is 60.

To find Jack's score, we substitute the value of x back into the equation:
Jack's score = 3x - 20 = 3(60) - 20 = 180 - 20 = 160.

Therefore, Jack's score is 160.

To solve the first problem, we need to set up a system of equations based on the given information.

Let's assume that the first number is represented by 'x' and the second number is represented by 'y'.

We are given two pieces of information:
1. The sum of the two numbers is 75. We can write this as an equation: x + y = 75.
2. The first number is 9 more than 5 times the second. We can write this as an equation: x = 5y + 9.

Now we have a system of equations:
x + y = 75
x = 5y + 9

To solve this system, we can use the method of substitution or elimination.

Let's use the method of substitution. We can substitute the value of x from the second equation into the first equation.

From the second equation, we have x = 5y + 9. Substitute this into the first equation:
(5y + 9) + y = 75

Simplifying: 6y + 9 = 75

Subtracting 9 from both sides: 6y = 66

Dividing both sides by 6: y = 11

Now that we have the value of y, we can substitute it back into one of the original equations to find x.

Using the equation x + y = 75, substitute y = 11:
x + 11 = 75

Subtracting 11 from both sides: x = 64

Therefore, the first number is 64.

Now let's move on to the second problem.

To solve the problem, we need to set up a system of equations based on the given information.

Let's assume Jack's score is represented by 'x' and Jill's score is represented by 'y'.

We are given two pieces of information:
1. Jack's score is 20 less than 3 times Jill's score. We can write this as an equation: x = 3y - 20.
2. The sum of their scores is 220. We can write this as an equation: x + y = 220.

Now we have a system of equations:
x = 3y - 20
x + y = 220

To solve this system, we can again use the method of substitution or elimination.

Let's use the method of substitution. We can substitute the value of x from the first equation into the second equation.

From the first equation, we have x = 3y - 20. Substitute this into the second equation:
(3y - 20) + y = 220

Simplifying: 4y - 20 = 220

Adding 20 to both sides: 4y = 240

Dividing both sides by 4: y = 60

Now that we have the value of y, we can substitute it back into one of the original equations to find x.

Using the equation x = 3y - 20, substitute y = 60:
x = 3(60) - 20

Simplifying: x = 180 - 20

x = 160

Therefore, Jack's score is 160 and Jill's score is 60.