# SAT Math : How to find the solution to an equation

## Example Questions

### Example Question #71 : How To Find The Solution To An Equation

A theme park charges $10 for adults and$5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of $3750? Possible Answers: 346 269 431 157 248 Correct answer: 346 Explanation: Let c = number of kids tickets sold. Then (548 – c) adult tickets were sold. The revenue from kids tickets is$5c, and the total revenue from adult tickets is $10(548 – c). Then, 5c + 10(548 – c) = 3750 5c + 5480 – 10c = 3750 5c = 1730 c = 346. We can check to make sure that this number is correct:$5 * 346 tickets + $10 * (548 – 346) tickets =$3750 total revenue

### Example Question #87 : Algebra

Two palm trees grow next to each other in Luke's backyard. One of the trees gets sick, so Luke cuts off the top 3 feet. The other tree, however, is healthy and grows 2 feet. How tall are the two trees if the healthy tree is now 4 feet taller than the sick tree, and together they are 28 feet tall?

14 and 14 feet

12 and 16 feet

8 and 20 feet

11 and 17 feet

cannot be determined

12 and 16 feet

Explanation:

Let s stand for the sick tree and h for the healthy tree. The beginning information about cutting the sick tree and the healthy tree growing is actually not needed to solve this problem! We know that the healthy tree is 4 feet taller than the sick tree, so h = s + 4.

We also know that the two trees are 28 feet tall together, so s + h = 28. Now we can solve for the two tree heights.

Plug h = s + 4 into the second equation: (s + 4) + s = 28. Simplify and solve for h: 2s = 24 so s = 12. Then solve for h: h = s + 4 = 12 + 4 = 16.

### Example Question #71 : Algebra

Solve for z

3(z + 4)3 – 7 = 17

4

8

2

–8

–2

–2

Explanation:

1. Add 7 to both sides

3(z + 4)3 – 7 + 7= 17 + 7

3(z + 4)3 = 24

2. Divide both sides by 3

(z + 4)3 = 8

3. Take the cube root of both sides

z + 4 = 2

4. Subtract 4 from both sides

z = –2

### Example Question #89 : Algebra

Jen and Karen are travelling for the weekend. They both leave from Jen's house and meet at their destination 250 miles away. Jen drives 45mph the whole way. Karen drives 60mph but leaves a half hour after Jen. How long does it take for Karen to catch up with Jen?

She can't catch up.

Explanation:

For this type of problem, we use the formula:

When Karen catches up with Jen, their distances are equivalent. Thus,

We then make a variable for Jen's time, . Thus we know that Karen's time is  (since we are working in hours).

Thus,

There's a logical shortcut you can use on "catching up" distance/rate problems. The difference between the faster (Karen at 60mph) and slower (Jen at 45mph) drivers is 15mph.  Which means that every one hour, the faster driver, Karen, gains 15 miles on Jen.  We know that Jen gets a 1/2 hour head start, which at 45mph means that she's 22.5 miles ahead when Karen gets started.  So we can calculate the number of hours (H) of the 15mph of Karen's "catchup speed" (the difference between their speeds) it will take to make up the 22.5 mile gap:

15H = 22.5

So H = 1.5.

### Example Question #90 : Algebra

Bill and Bob are working to build toys. Bill can build  toys in 6 hours. Bob can build  toys in 3 hours. How long would it take Bob and Bill to build  toys working together?

Explanation:

Bill builds  toys an hour. Bob builds  toys an hour. Together, their rate of building is . Together they can build  toys in 2 hours. They would be able to build  toys in 8 hours.

### Example Question #52 : Equations / Inequalities

Audrey, Penelope and Clementine are all sisters. Penelope is 8 years older than Clementine and 2 years younger than Audrey. If the sum of Penelope and Clementine's age is Audrey's age, how old is Clementine's age?

Explanation:

Let  = Audrey's age,  = Penelope's age, and  = Clementine's age.

Since , then .

Furthermore, , and .

Through substitution, .

### Example Question #1851 : Sat Mathematics

If   and , what is the value of ?

Explanation:

We could use the substitution or elimination method to solve the system of equations. Here we will use the elimination method.

To solve for , combine the equations in a way that makes the  terms drop out. The first equation has  and the second , so multiplying the first equation times 2 then adding the equations will eliminate the  terms.

Multiplying the first equation times 2:

Adding this result to the second equation:

Isolate  by dividing both sides by 7:

### Example Question #71 : Linear / Rational / Variable Equations

If   and , then what is the value of  ?