```Question 173678
these problems are linear equation problems
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1.lets call the number of units of plywood and lumber p and L respectively
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p=3L...eq 1
45(p)+30(L)=17160....eq 2
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take p's value from eq 1 and plug it into all the p's in eq 2
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45(3L)+30L=17160
:
135L+30L=17160
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165L=17160
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{{{highlight(L=104)}}}units of Lumber
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{{{highlight(p=3L=3(104)=312)}}}units of plywood
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2)lets call the 30 sec and 60 second spots t and s
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t+s=16.......eq 1---->t=16-s
1/2t+1s=13...eq 2---->t+2s=26(multiplied all terms by 2 to get rid of fraction)
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t+s=16.......eq 1
t+2s=26......eq 2 revised
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lets subtract eq 1 from eq 2 so as to eliminate the t terms t-t=0
we are left with 2s-s=26-16
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{{{highlight(s=10)}}}60 sec commercials
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{{{highlight(t=16-s=16-10=6)}}}30 sec commercials
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3)lets call the quarters and fifty cent pieces q and f respectively
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q+f=30.....eq 1
.25q+.5f=11.50....eq 2      20-9.50=change=11.50
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lets re write eq 1 . q=30-f now take q's value and plug it into eq 2
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.25(30-f)+.5f=11.5
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7.5-.25f+.5f=11.5
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.25f=4
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{{{highlight(f=16)}}}fifty cent pieces
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{{{highlight(q=30-f=30-16=14)}}}quarters
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4)remember perimeter equals 2 times the length plus 2 times the width
p=2L+2W where L and W are the length and width and p is the perimeter
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2L+2W=80.....eq 1
L=2W+7.......eq 2
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take L's value from eq 2 and plug it into eq 1
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2(2W+7)+2W=80
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4W+14+2W=80
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6W=66
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{{{highlight(W=11)}}}meters in width
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{{{highlight(L=2W+7=2(11)+7=29)}}}meters in length
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5)lets call the number of wins and ties , w and t respectively
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2w+1t=60....eq 1
w=t+9......eq 2
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take w's value from eq 2 and plug it into eq 1
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2(t+9)+t=60
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2t+18+t=60
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3t=42
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{{{highlight(t=14)}}}ties
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{{{highlight(w=t+9=14+9=23)}}}wins
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:hope that helps you out```