Linear / Rational / Variable Equations

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PSAT Math › Linear / Rational / Variable Equations

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Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

Explanation

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

What property of arithmetic is demonstrated here?

Reflexive

Transitive

Commutative

Identity

Symmetric

Explanation

The statement expresses the idea that any number is equal to itself. This is the reflexive property of equality.

If 5 + x is 5 more than 5,what is the value of 2_x_?

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

If 5 + x is 5 more than 5,what is the value of 2_x_?

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

Three consecutive even numbers add to 42. What is the middle number?

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

Explanation

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

Three consecutive even numbers add to 42. What is the middle number?

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

What property of arithmetic is demonstrated here?

Reflexive

Transitive

Commutative

Identity

Symmetric

Explanation

The statement expresses the idea that any number is equal to itself. This is the reflexive property of equality.

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