2m + 3c = 14.47
3m + 5c = 23.30
solve by substitution or elimination
At a local coffee shop, one customer purchased two muffins and three cups of coffee for
$14.47. Another customer ordered 3 muffins and 5 cups of coffee for $23.30. Write and
solve a system of equations to find the price of a single muffin and a single cup of coffee.
2 answers
Step 1. Subtract equations
(3M + 5C=23.3) - (2M + 3C= 14.47).
You get 1M + 2C = 8.83
Step 2. Do some arranging of the variables.
You get 1M= 8.83 - 2C. Presto! You can plug it in now to one of your original equations.
Step 3. Plug it in. I'll choose the first equation.
2(8.83-2C) + 3C= 14.47
Step 4. Multiply through.
17.66-4C+3C=14.47
Step 5. Clean it up.
-C=-3.19 which means C= 3.19
Alright I'm going to stop there. You should be able to find M with what I've given you.
(3M + 5C=23.3) - (2M + 3C= 14.47).
You get 1M + 2C = 8.83
Step 2. Do some arranging of the variables.
You get 1M= 8.83 - 2C. Presto! You can plug it in now to one of your original equations.
Step 3. Plug it in. I'll choose the first equation.
2(8.83-2C) + 3C= 14.47
Step 4. Multiply through.
17.66-4C+3C=14.47
Step 5. Clean it up.
-C=-3.19 which means C= 3.19
Alright I'm going to stop there. You should be able to find M with what I've given you.
1 answer