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put this solution on YOUR website!The larger of two numbers is 5 less than twice the smaller. their sum is 43. find the numbers:
Let the two numbers be x & y; x is the larger:
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Just translate the sentence to an equation: [the word "is" usually means "="]
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"Larger is 5 less than twice the smaller" ["5 less means '-5'"]
x = [2 * y] - 5
x = [2y - 5]
"Their sum is 43"
x + y = 43
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We know that x = [2y - 5], substitute [2y-5] for x:
[2y-5] + y = 43
3y = 43 + 5
y = 48/3
y = 16
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x = [2y -5]
x = 2(16) -5
x = 32-5
x = 27
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Check: 16 + 27 = 43
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2.the sum of two numbers is 75. the first is 9 more than 5 times the second. find the number
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Much the same as the first problem:
The first sentence: x + y = 75
For use later use: x = 75 - y
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"the first is 9 more than 5 times the second. "
x = 9 + (5*y)
x = [5y + 9}
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Now substitute [75-y] for x in the above equation:
75 - y = 5y + 9
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Solve for y just like we did in the first problem. check your solutions
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3.Jack's bowling score is 20 less than 3 times Jill's score. The sum of their scores is 220 find the score of each.
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Let Ja = Jack's score; Ji = Jill's score
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"Jack's score is 20 less than 3 time Jill's score":
Ja = 3*Ji - 20
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"Their sum of their scores is 220"
Ja + Ji = 220
Ja = 220 - Ji
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Substitute [220 - Ji] for Ja in the 1st equation and solve for Ji:
220 - Ji = 3*Ji - 20
220 + 20 = 3Ji + Ji
240 = 4Ji
Ji = 240/4
Ji = 60
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Ja = 220 - 60
Ja = 160
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Check: Ja = 3(60) - 20 = 160
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4. Jennifer cut a board 200cm long into two peices. One peice is 24cm shorter than the other. Find the length of each piece.
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Let one board = x; then other board has to be: [x - 24]
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The equation: x + [x-24] = 200
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You should be able so solve this now. Check your solutions
