Answer:
The decimal of 17/6=2.8333333333
Let's identify what we are looking for in terms of variables. Sandwiches are s and coffee is c. Casey buys 3 sandwiches, which is represented then by 3s, and 5 cups of coffee, which is represented by 5c. Those all put together on one bill comes to 26. So Casey's equation for his purchases is 3s + 5c = 26. Eric buys 4 sandwiches, 4s, and 2 cups of coffee, 2c, and his total purchase was 23. Eric's equation for his purchases then is 4s + 2c = 23. In order to solve for c, the cost of a cup of coffee, we need to multiply both of those bolded equations by some factor to eliminate the s's. The coefficients on the s terms are 4 and 3. 4 and 3 both go into 12 evenly, so we will multiply the first bolded equation by 4 and the second one by -3 so the s terms cancel out. 4[3s + 5c = 26] means that 12s + 20c = 104. Multiplying the second bolded equation by -3: -3[4s + 2c = 23] means that -12s - 6c = -69. The s terms cancel because 12s - 12s = 0s. We are left with a system of equations that just contain one unknown now, which is c, what we are looking to solve for. 20c = 104 and -6c = -69. Adding those together by the method of elimination (which is what we've been doing all this time), 14c = 35. That means that c = 2.5 and a cup of coffee is $2.50. There you go!
Answer:
a
Step-by-step explanation:
solve for y in one equation
2x + y = -4
y = -4 - 2x
plug y into the other equation
5x + 3y = -6
5x + 3(-4 - 2x) = -6
5x -12 -6x = -6
-x - 12 = -6
-x = 6
x = -6
plug x into the equation to find y
y = -4 - 2x
y = -4 - 2(-6)
y = 8
ordered pair: (-6,8)
Answer:the number of cars that were washed is 50
Step-by-step explanation:
Let x represent the number of cars that members of a senior class.
Let y represent the number of pick-up truck or a sport utility vehicle that members of a senior class.
They charged $3 to wash a car and $5 to wash a pick-up truck or a sport utility vehicle and they earned a total of $275. This means that
3x + 5y = 275 - - - - - - - - -- - -1
They washed a total of 75 vehicles. This means that
x + y = 75
Substituting x = 75 - y into equation 1, it becomes
3(75 - y) + 5y = 275
225 - 3y + 5y = 275
- 3y + 5y = 275 - 225
2y = 50
y = 50/2 = 25
Substituting y = 25 into x = 75 - y, it becomes
x = 75 - 25 = 50
