Answer: W = 112 carats
Step-by-step explanation: Let W be the original weight.
So we have
W - 45 = 67 add 45 to both sides
And that equals 112 carats
Answer:
There are 150 blue marbles in Alex's bag.
Step-by-step explanation:
Let 
, 
, 
be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:
Initial ratio
(1)
(2)
Final ratio
(3)
After some algebraic handling we get the following system of linear equations:
(1)
(2)
(3)
The solution of the system of linear equations is:
, 
, 
There are 150 blue marbles in Alex's bag.
Answer:
1 x 13 or 13 x 1
Step-by-step explanation:
13 is a prime number
When a figure is dilated, this means the corresponding sides of the shape is enlarged in a uniform multiple. In thsi case, the ratio of the sides remains the same. Thus, when ratio of the sides remains the same, the corresponding angles are also congruent in the dilated figure.
