Ms. Ervine has a basket of grapes.
If she gives 6 grapes to each of her students, she will have 2 grapes left.
If she gives 7 grapes to each of her students, she will have to buy 11 more grapes.
A) How many students does Ms. Ervine have?
B) How many grapes are in the basket?
number of students : n
number of grapes : x
6n + 2 = x
7n - 11 = x
7n - 11 = 6n + 2
n = 13
x = 6(13)+2 = 80
she has 13 students and 80 grapes
check:
6 grapes: 6(13) = 78 , she has 2 left over
7 grapes: 7(13) = 91 , she is 11 short
YEAH!!!
To find the answers to these questions, we need to set up a system of equations based on the given information.
Let's assume that the number of students Ms. Ervine has is represented by the variable "s," and the number of grapes in the basket is represented by the variable "g."
According to the first statement, if Ms. Ervine gives 6 grapes to each student, she will have 2 grapes left. This can be written as:
g - 6s = 2 -- Equation 1
According to the second statement, if Ms. Ervine gives 7 grapes to each student, she will have to buy 11 more grapes. This can be written as:
g - 7s = -11 -- Equation 2
Now we have a system of two equations. We can solve this system using the method of substitution or elimination.
Let's solve it using the substitution method:
From equation 1, we can rewrite it as:
g = 6s + 2
Substitute this expression for "g" in equation 2:
6s + 2 - 7s = -11
Combine like terms:
-s = -13
Multiply both sides by -1 to solve for "s":
s = 13
Therefore, Ms. Ervine has 13 students (answer to question A).
To find the answer to question B, substitute the value of "s" back into one of the original equations. Let's use equation 1:
g - 6(13) = 2
Simplify:
g - 78 = 2
Add 78 to both sides:
g = 80
Therefore, there are 80 grapes in the basket (answer to question B).