Writing 2 equations from the information given..

Question

A 500g slab of cheese is completely eaten by two mice.

If Minnie had eaten twice as much as she did, and Mickey had eaten half as much as he did, there would have been 100g left.

If Minnie = x and Mickey = y, use the information to get 2 equations relating x and y.

How much did each mouse eat?

Solve the problem algebraically.

 

 - Can you please show me the working out too? Thank you!!

Answer 1

                                                    *1/2=0.5

_{1.   x+y=500}

2.  2x +0.5y=500-100

 

Here is one way to work above equations.

                                 

1A          2x + 2y=1000     (x2 both sides)

2A          2x +0.5y=400    (do 500-100 and rewrite equetion 2)

1A-2A        1.5y=600 (substract equations, and solve for y)

                       y= 400

(Go back to 1 and use y=400)

      x+400=500

             x=500-400

             x=100

 

Or another way,

1. x+y=500
2. 2x +0.5y=500-100

 

1. (solve for y)  y=500-x

    (use y=500-x in the equation 2 and rewrite it and solve for x) 

   

    2x+0.5(500-x)=400

    2x+250-0.5x=400

                1.5x = 400-250

                1.5x =150

                     x=100

 

(use y=500-x, and x=100 to get y)

y=500-100

y=400