Question

Kiran is collecting dimes and quarters in a jar. He has collected $10 so far and has d dimes and q quarters. The relationship between the numbers of dimes and quarters, and the amount of money in dollars is represented by the equation 0.1d+0.25q=10

a. (100,0)
b. (20,50)
c. (50,20)
d. (0,100)
e.(10,36)

Answer 1

The equation 0.1d + 0.25q = 10 represents the relationship between the number of dimes and quarters collected by Kiran and the total amount of money collected. By rearranging the equation and substituting the answer choices, we can determine the correct solution.

Step-by-step explanation:

The equation 0.1d + 0.25q = 10 represents the relationship between the number of dimes (d) and quarters (q) collected by Kiran and the total amount of money collected ($10). To find the values of d and q, we can use the given equation.

First, let's rearrange the equation to solve for d:

d = (10 - 0.25q) / 0.1

Now, let's substitute the given answer choices into the equation to see if they satisfy the equation:

• a. (100,0): d = (10 - 0.25(0)) / 0.1 = 100
• b. (20,50): d = (10 - 0.25(50)) / 0.1 = -40
• c. (50,20): d = (10 - 0.25(20)) / 0.1 = 80
• d. (0,100): d = (10 - 0.25(100)) / 0.1 = 0
• e. (10,36): d = (10 - 0.25(36)) / 0.1 = 64

From the calculations, we can see that the only answer choice that satisfies the equation is (0,100). Therefore, the correct answer is d. (0,100).