This problem provides you with a classic SAT Systems of Equations setup. You're given the sum of two entities - here that's Blin's Total + Alex's Total = $240,000 - and a relationship between those two entities. Here that's Blin raised $60,000 more than Alex did.

The sum equation is generally straightforward; you can express that as B + A = 240,000. For the relationship equation, you can say that Blin's total is $60,000 more than Alex's, which translates to B = 60,000 + A.

Now you have two equations:

B + A = 240,000

B = 60,000 + A

This structure sets up well for Substitution; you already have B in terms of A, so you can plug in the second equation for the first:

(60,000 + A) + A = 240,000

60,000 + 2A = 240,000

2A = 180,000

A = 90,000

Of course, at this point you need to check whether you solved for the proper variable. The question asks you about Blin's total, not Alex's, so you need to add $60,000 to get to Blin's total of $150,000. Then check your work: does Blin's total of $150,000 plus Alex's total of $90,000 arrive at the sum we know to be $240,000? It does, so you can confidently choose $150,000.

This word problem starts you off with two equations. If you assign variables as = bats and = balls, you have:

, which reduces to

and

You can then use the Elimination Method to eliminate the terms and solve for :

, so . Plug that back in, and . So now you have the prices.

At this point, you know that you need the same number of and , and that the total can only be as high as $240. If you call that same number , you have:

. So you'll be able to buy 4 bats and 4 balls.

Whenever you're facing a unit conversion problem it is a good idea to use dimensional analysis to help you structure the math - whether you should multiply or divide by the provided conversion ratio - properly. That means that you'll set up the math such that the units you don't want in your answer cancel, leaving you with the units you do want. Here you're given quarts but asked to convert to pints, so you'll set up the math so that quarts are in the denominator and cancel, leaving you with pints:

This means that quarts cancel leaving you with pints, and tells you that you have to multiply 12 by 2. The correct answer is 24.

To begin on this problem, first take of 480 to determine that there are currently 120 hybrid cars. So if half were to be sold, then that would leave 60 hybrids.

Importantly, note that if 60 hybrids are sold, that means that 60 of the total of 480 cars are sold. That affects both the number of hybrids AND the number of total cars, which is now reduced to 420. So your new proportion of hybrids is the 60 hybrids out of the 420 total cars:

The key here is to ensure your units cancel out. .

This problem provides you with a classic SAT Systems of Equations setup. You're given the sum of two entities - here that's Blin's Total + Alex's Total = $240,000 - and a relationship between those two entities. Here that's Blin raised $60,000 more than Alex did.

The sum equation is generally straightforward; you can express that as B + A = 240,000. For the relationship equation, you can say that Blin's total is $60,000 more than Alex's, which translates to B = 60,000 + A.

Now you have two equations:

B + A = 240,000

B = 60,000 + A

This structure sets up well for Substitution; you already have B in terms of A, so you can plug in the second equation for the first:

(60,000 + A) + A = 240,000

60,000 + 2A = 240,000

2A = 180,000

A = 90,000

Of course, at this point you need to check whether you solved for the proper variable. The question asks you about Blin's total, not Alex's, so you need to add $60,000 to get to Blin's total of $150,000. Then check your work: does Blin's total of $150,000 plus Alex's total of $90,000 arrive at the sum we know to be $240,000? It does, so you can confidently choose $150,000.

Whenever you're facing a unit conversion problem it is a good idea to use dimensional analysis to help you structure the math - whether you should multiply or divide by the provided conversion ratio - properly. That means that you'll set up the math such that the units you don't want in your answer cancel, leaving you with the units you do want. Here you're given quarts but asked to convert to pints, so you'll set up the math so that quarts are in the denominator and cancel, leaving you with pints:

This means that quarts cancel leaving you with pints, and tells you that you have to multiply 12 by 2. The correct answer is 24.

This word problem starts you off with two equations. If you assign variables as = bats and = balls, you have:

, which reduces to

and

You can then use the Elimination Method to eliminate the terms and solve for :

, so . Plug that back in, and . So now you have the prices.

At this point, you know that you need the same number of and , and that the total can only be as high as $240. If you call that same number , you have:

. So you'll be able to buy 4 bats and 4 balls.

To begin on this problem, first take of 480 to determine that there are currently 120 hybrid cars. So if half were to be sold, then that would leave 60 hybrids.

Importantly, note that if 60 hybrids are sold, that means that 60 of the total of 480 cars are sold. That affects both the number of hybrids AND the number of total cars, which is now reduced to 420. So your new proportion of hybrids is the 60 hybrids out of the 420 total cars:

The key here is to ensure your units cancel out. .