can u please help with the problem below??

Question

can u help me solve the word problem below??

in one game Monte scored twice as many points as Rick. In the next game Monte scored 6 fewer points than he did in the first game, while Rick scored 9 more points than he did in the first game. if they both scored the same number of points in the second game, what were their scores in the first game?

Answer 1

Let us say that  X₁ represents the number of points that Monte scored in the first game, and

X₂ represents the number points that Monte scored in the second game. Likewise,

let Y₁ represent the number of points that Rick scored in the first game, and

let Y₂ represent the number of points that Rick scored in the second game.

(Gee, it's too bad that Rick's name wasn't actually Carlo. Then we could talk about these

as being Monte / Carlo games. But I digress...)

 

We have 4 equations in 4 unknowns, that we can solve:

 

1)   X₁  =  2 * Y₁

2)   X₂  =  Y₂  

3)   X₂  = X₁  -  6

and

4)   Y₂  =  Y₁  +  9

 

You can substitute equations 3 and 4 into equation 2 and simplify, solving for X₁ in terms of Y₁, or

for Y₁ in terms of X₁.

Then you can substitute that equation into equation 1 and solve for the remaining variable, X₁ or Y₁.

 

Go back to equation 1 with your newly found value, and solve for the other variable.

 

Answer 2

Hi Maddie,

 

You need to translate the English into math. . .

Let M=Monte's points

Let R = Rick's points

 

In one game Monte scored twice as many points as Rick so 2R = M . . . if Rick scored 10 points, then Monte scored 20 points.

 

In the next game Monte scored 6 fewer points so that's M - 6

and Rick scored 9 more points so that's R + 9

and they scored the same number of points in the second game so M-6=R+9

 

The first equation says that 2R = M so we can substitute 2R for M in the last equation . . .

 

2R -6 = R + 9

 

Now we have the same variable in this equation. . .

 

Rewriting it so the R terms are on the left and the numbers are on the right. . .

 

2R - R = 9 + 6

R = 15

so M = 30

 

Plug these numbers into the second equation to make sure they work.

 

Have fun.

 

Dan