Question 391·Easy·Algebra

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If $5p - 3 = 27$ , what is the value of $15p - 9$ ?

If a question gives the value of one expression and asks for a related one, check for a common factor before solving for the variable. When both terms have been multiplied by the same number, multiply the whole known value by that number. Scaling only the variable term, or subtracting the constant again, changes the expression.

Hints

Hint 1
A factor multiplies a whole expression. Compare both the term with $p$ and the constant in the requested expression with those in the equation. Did both change by the same factor?
Hint 2
Once you write the requested expression as a multiple of $5p-3$ , use the given value of that whole expression. You don't need to find $p$ .

Step-by-step

Approach 1: Scale the whole expression
Step 1
Find the shared factor
No Desmos needed. The requested expression is a multiple of the equation's whole left side. Both $5p$ and $-3$ are multiplied by $3$ to make $15p$ and $-9$ . Factor out $3$ to show the whole expression being scaled:
$15p-9=3(5p-3).$
Scale both terms, not only the term with $p$ .
Step 2
Use the value already given
The equation says $5p-3=27$ , so replace the entire parenthesis with $27$ :
$15p-9=3(27).$
Multiply by $3$ :
$15p-9=81.$
That is the value of the requested expression. Choice D.

Approach 2: Solve for $p$ in Desmos
Step 1
Find the variable's value
If you don't spot the scaling, type $5p_{1}-3\sim27$ in Desmos. The $\sim$ asks Desmos to find the value of $p_{1}$ that makes the two sides equal. Under PARAMETERS, it reports $p_{1}=6$ .
Step 2
Evaluate what the question asks for
Keep the first line and type $15p_{1}-9$ . Desmos prints $81$ , the value of $15p-9$ . Solving for $p$ works, but the scaling shortcut avoids that extra solve. Choice D.

Lessons that teach this

SAT AlgebraBeginnerCoreSolve linear equations

Question 391·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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