4. Ricky bobby and Betty Sue want to go the San Diego Fair. They want to spend all day going on the rides. When
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For this case we propose a system of equations:
x: Let the variable representing the age of the first child of the Smiths
y: Let the variable representing the age of the second child of the Smiths
According to the data of the statement we have to:
From the first equation we have to:
We substitute in the second equation:
We find the solutions by factoring:
We look for two numbers that, when multiplied, result in 132 and when added, result in 23. These numbers are 11 and 12.
Thus, we have that the factorized equation is:
Thus, the solutions are:
So, we can take any of the solutions:
With
Then
Therefore, the ages of the children are 11 and 12 respectively.
Answer:
The ages of the children are 11 and 12 respectively.
A) For the equation 
, the slope is 
.
Slope-intercept form is y = mx + b, where m is slope and b is the y-intercept. This means that if
, the slope is .
B) Since this equation is in the same form, you just find what m is equal to.
Since
, that's the slope.
For the solution, set equal to 
, so it would be put together like this:
![y=[tex]- \frac{1}{2}x+3=2x-4\\ -\frac{1}{2}=2x-7\\ 1\frac{1}{2}x=-7\\ x=-4.66667](https://tex.z-dn.net/?f=y%3D%5Btex%5D-%20%5Cfrac%7B1%7D%7B2%7Dx%2B3%3D2x-4%5C%5C%20-%5Cfrac%7B1%7D%7B2%7D%3D2x-7%5C%5C%201%5Cfrac%7B1%7D%7B2%7Dx%3D-7%5C%5C%20x%3D-4.66667)
So your answer is -4.667.
Slope-intercept form is y = mx + b, where m is slope and b is the y-intercept. This means that if
B) Since this equation is in the same form, you just find what m is equal to.
Since
For the solution, set
So your answer is -4.667.