Henry has a collection of dimes and quarters totaling $47.50. The number of quarters is 10 more than twice the number of dimes. If d represents the number of dimes and q represents the number of quarters, select the system of equations described by the scenario.(1 point)

Question

Responses

{10d+25q=47.50q=2d+10
enlarged left brace start layout first row 10 d plus 25 q equals 47.50 second row q equals 2 d plus 10 end layout

{d+q=47.50q=2d+10
enlarged left brace start layout first row d plus q equals 47.50 second row q equals 2 d plus 10 end layout

{0.10d+0.25q=47.50q=2(d+10)
enlarged left brace start layout first row 0.10 d plus 0.25 q equals 47.50 second row q equals 2 left parenthesis d plus 10 right parenthesis end layout

{0.10d+0.25q=47.50q=2d+10

Answer 1

To formulate the system of equations based on the scenario described, we need to represent the total amount of money in terms of dimes and quarters, as well as the relationship between the number of dimes and quarters.

1. Total value equation: The value of dimes (10 cents each) and quarters (25 cents each) totals $47.50. This can be expressed as: \[ 0.10d + 0.25q = 47.50 \]

2. Relationship equation: The number of quarters (q) is 10 more than twice the number of dimes (d). This relationship is expressed as: \[ q = 2d + 10 \]

Thus, the system of equations based on the scenario is: \[ \begin{cases} 0.10d + 0.25q = 47.50 \ q = 2d + 10 \end{cases} \]

The correct response from the options provided is: {0.10d + 0.25q = 47.50 \ q = 2d + 10}