1985 AHSME Problems/Problem 1

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Problem

If $2x+1=8$, then $4x+1=$

$\mathrm{(A)\ } 15 \qquad \mathrm{(B) \ }16 \qquad \mathrm{(C) \  } 17 \qquad \mathrm{(D) \  } 18 \qquad \mathrm{(E) \  }19$

Solution

Solution 1

From $2x+1=8$, we subtract $1$ from both sides to get $2x=7$. We can divide both sides now by $2$ to get $x=\frac{7}{2}$. Now we can substitute this into $4x+1$ to get $4x+1=4\left(\frac{7}{2}\right)+1=(2)(7)+1=14+1=15, \boxed{\text{A}}$.

Solution 2

We proceed from $2x=7$ as above. Notice that $4x=2(2x)=2(7)=14$, so $4x+1=14+1=15, \boxed{\text{A}}$.

See Also

1985 AHSME (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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