Question 62036: (1) A history instructor is undecided on the amount of weight to give each type of question on his test, but knows that because of time restrictions, he can only ask a certain number of each type. If multiple-choice questions are worth 7 points each and the true-false questions worth 2 points each, the test will be worth a total of 185 points. If the multiple-choice and true-false questions are worth 4 points each, the test will be worth a total of 200 points. Find the number of multiple-choice questions and the number of true-false questions that he will have on the test.
(2) My friend and I went out to lunch last week, but we did not pay attention to the cost of each item we ordered until we compared receipts. I had one soft drink and one taco. My bill showed a tax of 15 cents and a total of $2.25. My friend had two soft drinks and three tacos. His bill showed a tax of 36 cents and a ottal of $5.51. How much was each item (before tax)?
(3) Given below are two equivalent systems of equations. Find the value of A and B.
x + 2y = 2
5x - 3y = -29
and
Ax + 5y = -9
x + By = 8
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A history instructor is undecided on the amount of weight to give each type of question on his test, but knows that because of time restrictions, he can only ask a certain number of each type. If multiple-choice questions are worth 7 points each and the true-false questions worth 2 points each, the test will be worth a total of 185 points. If the multiple-choice and true-false questions are worth 4 points each, the test will be worth a total of 200 points. Find the number of multiple-choice questions and the number of true-false questions that he will have on the test
:
Let x = no. of mult choice; y = no. of true/false
1st case:
7x + 2y = 185
2nd case:
4x + 4y = 200
:
Mult the 2nd equation by .5 and subtract it from the 1st equation
7x + 2y = 185
2x + 2y = 100
--------------
5x + 0y = 85
x = 85/5
x = 17 mult ch questions
:
Find the true/false using the 1st equation
7(17) + 2y = 185
119 + 2y = 185
2y = 185 - 119
2y = 66
y = 33 true/false questions
:
Check solutions in the 2nd equation:
4(17) + 4(33) = 200
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(2) My friend and I went out to lunch last week, but we did not pay attention to the cost of each item we ordered until we compared receipts. I had one soft drink and one taco. My bill showed a tax of 15 cents and a total of $2.25. My friend had two soft drinks and three tacos. His bill showed a tax of 36 cents and a total of $5.51. How much was each item (before tax)?
:
Subtract the taxes from both totals and we have 2.10 and 5.15
Let x = drinks; y = tacos
:
1x + 1y = 2.10
and
2x + 3y = 5.15
:
Mult 1st equation by 2 and subtract, solve for y
2x + 3y = 5.15
2x + 2y = 4.20
-----------------subtract
0x + y = .95 is the cost of a taco
:
I'll let you fiqure out the drink cost from the 1st equation
Check your solutions in the 2nd equation.
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(3) Given below are two equivalent systems of equations. Find the value of A and B.
x + 2y = 2
5x - 3y = -29
:
Solve the above sytem for x & y,
Use elimination, mult the 1st eq by 3 and the 2nd equation by 2:
3x + 6y = 6
10x - 6y = -58
------------------add
13x + 0y = -52
x = -52/13
x = -4
:
Find y using x + y = 2
-4 + 2y = 2
2y = 2 + 4
y = 6/2
y = + 3
:
:
Substitute -4 for x and +3 for y in the following to find a & b
A(-4) + 5(3) = -9
-4A = 15 = -9
-4A = -9 - 15
-4a = -24
a = -24/-4
a = + 6
:
Find B:
-4 + B(3) = 8
3B = 8 + 4
B = 12/3
B + +4
:
Did all this make sense to you??
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