Final answer:
To find how many chicken and steak tacos they ordered, we need to solve a system of equations. The equation 3C + xS = 48 represents the total cost of their order, and the equation S = C + 5 represents the difference in the number of steak and chicken tacos. By substituting values, we can find that they ordered 5 chicken tacos and 8 steak tacos.
Step-by-step explanation:
Let's denote the number of chicken tacos as C and the number of steak tacos as S.
According to the problem, S = C + 5, and the total cost of their order is $48.
The cost of chicken tacos is $3 each, so the cost of C chicken tacos is 3C.
The cost of steak tacos is $x each, so the cost of S steak tacos is xS.
Therefore, we have the equation:
3C + xS = 48
We also know that S = C + 5, so we can substitute this into the equation:
3C + x(C + 5) = 48
Simplifying the equation:
3C + xC + 5x = 48
Combining like terms:
(3 + x)C + 5x = 48
Now, we need to find the values of C and x that satisfy this equation.
Since there are infinitely many solutions to this equation, we can choose any value for C and find the corresponding value of x.
For example, let's choose C = 5.
Substituting C = 5 into the equation, we have:
(3 + x)(5) + 5x = 48
15 + 5x + 5x = 48
10x + 15 = 48
10x = 33
x = 3.3
So, if they ordered 5 chicken tacos and 8 steak tacos (C = 5, S = C + 5 = 10), the equation is satisfied and the total cost of their order is $48.