2) The sum of the measures of angle X and angle Y is 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X?A) 20B) 35C) 50D) 653) The yearbook club is having a bake sale to raise money for the senior class. Large cupcakes are sold for $1.25 each and small cupcakes are sold for $0.75 each. If 105 cupcakes were sold for a total amount of $109.75, how many large cupcakes did the yearbook club sell?A) 43B) 55C) 62D) 164) Solve the following system of equations using substitution. What is the value of y?2x+3y=105x+2y=65A) 15B) 20C) 40D) 65
Accepted Solution
A:
2) The answer is C. 50.
In order to solve this you need to represent the measure of x in terms of y. Since x is 30 less than twice as big as y, we can express it using the following: 2y - 30.
Now we can add that to y and set equal to 90 to solve. 2y - 30 + y = 90 3y - 30 = 90 3y = 120 y = 40.
Now knowing that y = 40, we know that x = 50, since they add up to 90.
3) They sold 62 large cupcakes.
This can be found by setting up a system of equations.
The first equation should represent the number sold totally. x + y = 105, where x is equal to the number of large cupcakes and y is equal to the number of small cupcakes.
The second equation should be equal to the amount of money made. 1.25x + .75y = 109.75.
Now to solve this system, you need to multiply the first equation by -1.25. This will give us a new equation of -1.25x - 1.25y = -131.25.
Now if you add the new equation to the second equation, the x values will cancel, giving you the following: -.5y = -21.5 or y = 43.
We can then determine the number of large cupcakes (x) by subtracting our y value from the 105 total, leaving us with 62.
4) The answer for this question is none of your possible answers. The y value should be 25 (the x-value though should be 15, which is the A answer).
We can find this by solving the second equation for x. x + 2y = 65 x = -2y + 65.
Now that we have a value for x, we can sub it into the first equation in place of x and solve for y. 2x + 3y = 105 2(-2y + 65) + 3y = 105 -4y + 130 + 3y = 105 -y + 130 = 105 -y = -25 y = 25.