Answer:
1. The two numbers are 15 and 12.
2. 0.1x + 0.25y = 4 and x = y + 5
3. Roberta has 15 dimes and 10 quarters.
Step-by-step explanation:
1. Let one number is x and the other number is y.
Now, the sum of the two numbers is 27 and one number is 3 more than the other number.
Hence, from those two conditions we can write two equations as
x + y = 27 ......... (1) and
x = y + 3 .......... (2) where x > y.
Now, solving those two equations we get,
(y + 3) + y = 27
⇒ 2y = 24
⇒ y = 12
Hence, from equation (2) we get, x = 12 + 3 = 15
Therefore, the two numbers are x = 15 and y = 12. (Answer)
2. Let Roberta has y number of quarters and x number of dimes.
Now, 1 dime = 0.1$ and 1 quarter = $0.25
Given that, she has $4 in dimes and quarters.
So, 0.1x + 0.25y = 4 ........ (3)
Again, given that she has 5 more dimes than quarters.
So, x = y + 5 ........... (4)
Therefore, those are the two equation from which we can calculate the number of dimes and the number of quarters she has. (Answer)
3. Solving equations (3) and (4) from part 2, we get,
0.1(y + 5) + 0.25y = 4
⇒ 0.35y = 4 - 0.5 = 3.5
⇒ y = 10
Now, from equation (4) we get, x = y + 5 = 15
Therefore, Roberta has 15 dimes and 10 quarters. (Answer)
