The ratio of staff to patients at Lakeview is 8 to 7. If total staff plus patients is 1575 people,
how many staff are at Lakeview?
help me get started on how to solve this
The ratio of staff to patients is 8:7. The total is 1575.
Add 8+7 = 15, and divide the total by the total of the ratio.
1575/15 = 105
Now multiply 103 by 8 to find the number of staff: 840
Let s = # staff
let p = # patients
================
s/p = 8/7
s+p= 1575
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Two equations; two unknowns.
To solve this problem, you need to set up a proportion based on the given ratio of staff to patients. Here's how you can get started:
Step 1: Define the variables.
Let's assume that the number of staff is represented by "x."
Step 2: Express the ratio in terms of variables.
The ratio of staff to patients is given as 8 to 7, which can be written as x/7 since we defined the number of staff as "x."
Step 3: Set up the proportion.
Since the total staff plus patients is 1575, the equation becomes:
x + 7 = 1575
Step 4: Solve for "x".
Isolating the variable "x," it becomes:
x = 1575 - 7
x = 1568
Therefore, there are 1568 staff members at Lakeview.
To solve this problem, you need to set up and solve an equation based on the given information.
Let's designate the number of staff as "S" and the number of patients as "P." We know that the ratio of staff to patients is 8 to 7, which can be written as:
S/P = 8/7
We are also provided with the total number of staff and patients combined, which is 1575 people:
S + P = 1575
To find the number of staff at Lakeview, we need to isolate the value of S in one of the equations. We can do this by rearranging the second equation to solve for P:
P = 1575 - S
Now substitute this value of P into the first equation:
S / (1575 - S) = 8/7
To solve for S, we can cross-multiply:
7S = 8(1575 - S)
Now distribute 8 across the parentheses:
7S = 12600 - 8S
Next, combine like terms:
7S + 8S = 12600
Simplify:
15S = 12600
Finally, divide both sides of the equation by 15:
S = 12600 / 15
Simplify further:
S = 840
Therefore, there are 840 staff members at Lakeview.