To find the number of quarters Sarah has, we can set up and solve a system of equations. Let q be the number of quarters and d be the number of dimes. Using the given information, we can set up two equations and solve for q. The number of quarters Sarah has is 425.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's represent the number of quarters and dimes as variables:
Let q be the number of quarters and d be the number of dimes.
From the information given, we know that:
1. q + d = 600 (since Sarah has 600 quarters and dimes in total)
2. 0.25q + 0.10d = 123.75 (since the value of 600 quarters and dimes is $123.75)
Solving the system of equations:
Using the substitution method, we can express one variable in terms of the other and substitute it into the other equation:
From equation 1, q = 600 - d.
Substituting q in equation 2:
0.25(600 - d) + 0.10d = 123.75
150 - 0.25d + 0.10d = 123.75
150 - 0.15d = 123.75
0.15d = 150 - 123.75
0.15d = 26.25
d = 26.25 / 0.15
d = 175
Therefore, Sarah has 175 dimes. Now we can substitute this value into equation 1 to find the number of quarters:
q + 175 = 600
q = 600 - 175
q = 425
Therefore, Sarah has 425 quarters.
The probable question can be: Sarah has 600 quarters and dimes in her piggy bank which totals $123.75. How many quarters does she have?