Arnold’s golf score was 12 strokes less than jacks. The sum of their scores was 150. What were their scores

Answer 1

For this problem, we will need to form two equations so that we can have a system of equations.

Let's make A = Arnold and J = Jack.

The problem states that Arnold's golf score is 12 strokes less than Jack's. From this, the first algebraic equation is: A = J - 12

The problem also states that the sum of Arnold's and Jack's scores is 150. From this, the second algebraic equation is: A + J = 150

So, our system of equations is:

1st) A = J - 12

2nd) A + J = 150

We need to solve for A and J. First, we can solve for J but using the substitution method. Substitute the 1st equation into the 2nd equation:

A + J = 150

(J - 12) + J = 150 Substitute.

2J - 12 = 150 Combine like terms.

2J = 162 Add 12 to both sides.

J = 81 Divide both sides by 2.

We find that Jack's score is 81.

To find Arnold's score, we substitute 81 into either the 1st or 2nd equation. You will get the same answer whichever equation you choose. Let's do the 1st equation:

A = J - 12

A = 81 - 12

A = 69

Arnold's score is 69.

Answer:

Arnold: 69 strokes

Jack: 81 strokes

Answer 2

Let us set up some variables to represent Arnold's and Jack's scores:

a = Arnold's score

j = Jack's score

We know that Arnold's score (a) is 12 less than Jack's score (j). We can convert this into math symbols by knowing "is" means equal (=) and "less than" means subtract (-). From here we get:

a = j - 12

We are also told that the sum (+) of their scores was 150, meaning we have to add their scores together.

a + j = 150

By using substitution, we can use both the equations to make one equation!

a + j = 150 (substitute a = j - 12)

j - 12 + j = 150 (combine like terms by adding the j's and then adding the 12 to both sides)

2j = 162 (We want to have j by itself, we have to get the 2 to the other side by dividing)

j = 81

Now we know Jack's score is 81! What about Arnold's score?

Let's use the first equation we found:

a = j - 12 (substitute j = 81)

a = 81 - 12

a =69

Now we have Arnold's score too!

-Fred

Answer 3

Greetings! Lets solve this shall we?

Lets Arnold's score be A = J - 12 and the sum of their scores be equal to 150 such that A + J = 150. Now, we can solve the problem to find each of their scores!

Replace (J-12) into A + J = 150 to become (J-12) + J = 150. Then 2J - 12 = 150. Then we add 12 to both sides such that 2J = 162. Finally, we divide 2 to get J = 81! So Jack's score was 81!

Then, we substitute Jack's score into the equation A + (81) = 150 to obtain Arnold's score. Now we subtract 81 to both sides to see Arnold had a score of A = 150 - 81 = 69 !

I hope this helped!

Answer 4

Great question! When dealing with story problems, we need to assign variables. Let's say "x" is Jack's golf score. We know that Arnold's golf score is 12 strokes less than Jack's. So:

Jack's score = x

Arnold's score = x - 12

Their sum (addition) is 150:

Jack's score + Arnold's score = 150

x + x - 12 = 150

2x - 12 = 150

+12 +12

2x = 162

x = 81

So, Jack's score was 81 while Jack's score was 69.