The price of a chicken sandwich was $6.80 and the price of a beef sandwich was $9.80 without GST. Ahmad bought a total of 90 chicken and beef sandwiches and paid $815.34 including 7% of GST. How many beef sandwiches did Ahmad buy?
Let's represent the number of chicken sandwiches as c and the number of beef sandwiches as b.
The total cost of chicken sandwiches is 6.8c.
The total cost of beef sandwiches is 9.8b.
So the total cost of all sandwiches without GST is 6.8c + 9.8b.
The total cost of all sandwiches including GST is 1.07 * (6.8c + 9.8b).
We can set up the following equation: 1.07 * (6.8c + 9.8b) = 815.34.
Expanding the equation, we get 7.276c + 10.486b = 815.34.
Since Ahmad bought a total of 90 sandwiches, we know that c + b = 90.
We can rearrange this equation to c = 90 - b.
Substituting this into the first equation, we get 7.276(90 - b) + 10.486b = 815.34.
Expanding the equation further, we get 654.84 - 7.276b + 10.486b = 815.34.
Combining like terms, we get 2.21b = 160.5.
Dividing both sides by 2.21, we get b = 72.45.
Since we can't buy a fraction of a sandwich, Ahmad must have bought 72 therefore beef sandwiches. Answer: \boxed{72}.
90 chicken and beef sandwiches = 40 chicken sandwiches + 50 beef sandwiches
50 beef sandwiches x 9.80 = 490
40 chicken sandwiches x 6.80 = 272
490 + 272 = 762
GST = 815.34 - 762 = 53.34
53.34 / 0.07 = 762.
Therefore, 50 beef sandwiches were bought.
Apologies for the previous incorrect response.
To clarify,
Let the number of chicken sandwiches be c and the number of beef sandwiches be b.
From the information given, we know that c + b = 90 and the total cost of all sandwiches without GST is 680c + 980b.
The total cost of all sandwiches including GST is 815.34.
We can set up the following equation:
680c + 980b + GST = 815.34.
We need to find the value of b.
Given that Ahmad only bought beef and chicken sandwiches, we can rewrite the equation as:
680(90 - b) + 980b + GST = 815.34.
Simplifying the equation, we get:
61200 - 680b + 980b + GST = 815.34.
Combining like terms, we get:
300b + GST = 815.34 - 61200,
300b + GST = 53.34.
To find the value of GST, we divide by 1.07:
GST = 53.34 / 1.07 = 49.91.
Substituting back into the equation, we have:
300b + 49.91 = 815.34 - 61200,
300b = 815.34 - 61200 - 49.91,
300b = 764.43,
b = 764.43 / 300,
b ≈ 2.55.
Since we can't buy a fraction of a sandwich, Ahmad must have bought 2 beef sandwiches.
Therefore, Ahmad bought 2 beef sandwiches.
Let's assume that Ahmad bought x chicken sandwiches and y beef sandwiches.
The price of a chicken sandwich without GST is $6.80.
So, the cost of x chicken sandwiches without GST is 6.8x.
The price of a beef sandwich without GST is $9.80.
So, the cost of y beef sandwiches without GST is 9.8y.
The total cost of chicken and beef sandwiches without GST is 6.8x + 9.8y.
Ahmad paid a total of $815.34, including 7% GST.
So, the total cost of chicken and beef sandwiches, including GST, is 1.07(6.8x + 9.8y).
According to the given information, the total number of sandwiches bought is 90.
So, x + y = 90.
Putting it all together, we have the system of equations:
6.8x + 9.8y = total cost without GST
1.07(6.8x + 9.8y) = total cost with GST
x + y = 90
To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method.
Multiplying the first equation by 1.07:
1.07(6.8x) + 1.07(9.8y) = 1.07(total cost without GST)
Simplifying, we get:
7.276x + 10.486y = total cost with GST
Now we can form the new system of equations:
6.8x + 9.8y = total cost without GST
7.276x + 10.486y = total cost with GST
x + y = 90
To eliminate the decimals in the second equation, we can multiply the second equation by 1000:
7276x + 10486y = 1.07(total cost with GST)
Now we have the system of equations:
6.8x + 9.8y = total cost without GST
7276x + 10486y = 1070(total cost with GST)
x + y = 90
We can now solve this system of equations.