Question

The school cafeteria sells three different types of sandwiches: chicken, turkey,

and roast beef. Chicken sandwiches sell for $3, turkey sandwiches sell for

$3.50, and roast beef sandwiches sell for $4. The cafeteria makes 400

sandwiches in total, and, if all sandwiches are sold, the cafeteria will take in

$1375. If the cafeteria makes the same number of chicken sandwiches as it

does turkey sandwiches, how many of each type of sandwich does the school

make? (Hint: Write one equation for the number of sandwiches, one equation

for to amount of money all the sandwiches cost, and an equation that show the

number of chicken and turkey sandwiches are equal.)

No

Answer 1

Number of chicken sandwiches = 150

Number of turkey sandwiches = 150

Number of roast beef sandwiches= 100

Explanation:

We are told the school cafeteriat makes and sells 3 different types of sandwiches which are; chicken, turkey and roast beef.

Let chicken be x, turkey be y and roast beef be z.

We are told they make 400 sandwiches in total.

Thus;

x + y + z = 400

However, we are told that the cafeteria makes same number of chicken and turkey sandwiches.

Thus, x = y

Thus;

Total is now;

x + x + z = 400

2x + z = 400 - - - (eq 1)

Now,we are told that chicken, turkey and roast beef sandwiches are sold for $3, $3.5 and $4 respectively. Also that the total amount realized from sales is $1375.

Thus;

3x + 3.5y + 4z = 1375

Since x = y. Thus;

3x + 3.5x + 4z = 1375

6.5x + 4z = 1375 - - - (eq 2)

Let's make z the subject in eq 1.

Thus;

z = 400 - 2x - - - (eq 3)

Putting 400 - 2x for z in eq(2) gives us;

6.5x + 4(400 - 2x) = 1375

6.5x + 1600 - 8x = 1375

1600 - 1375 = 8x - 6.5x

225 = 1.5x

x = 225/1.5

x = 150

Putting 150 for x in eq 3 gives;

z = 400 - 2(150)

z = 400 - 300

z = 100

Since x = y. Then y = 150