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## Digital SAT Math

### Course: Digital SAT Math>Unit 2

Lesson 6: Systems of linear equations word problems: foundations

# Systems of linear equations word problems — Harder example

Watch Sal work through a harder Systems of linear equations word problem.

## Want to join the conversation?

• Agnes has 23 collectible stones, all of which are labradorite crystals or galena crystals. Labradorite crystals are worth \$20 each, while galena crystals are worth \$13 each. Agnes earns \$439 by selling her entire collection. How many stones of each type did she sell? • good concept but a little bit confusing • Why are we given harder practice problems then what the example shows? This one looks more simple, but the other practice problems are so complicated sometimes. The SAT is coming soon, I just feel so under prepared.. • you can solve it with less time and effort. you can substract 4 children and 1 adult from each choice and see if the remaining children are double the adults since each of the remaining adults brought 2 children. think smarter not harder haha • how can we use this for graphs? • Hi, is this problem you immediately knew that there will be only 1 adult with two kids so you did the math of 4+2x2=8.
I thought, however, that there will be two adults (parents) as my fist logical thing to think.
how could one understand that there is only one adult for each 2 kids?

thanks! • I just solved this question by constructing the following equations and got the same answer

4 + 2(a-1)= c
2c + 4a= 60 • Here is my way of solving it:
We know that they charge \$2 for each child and \$4 for each adult and the total ticket sales from the children and adults was \$60.

2c + 4a = 60

We know that there is an adult that brought 4 children and the remaining adults brought 2 children each.

c = 4 + 2 (a-1)

Let's substitute that into the first equation.
=> 2c + 4a = 60
=> 2 (4 + 2[a-1]) + 4a = 60
=> 2 (4 + 2a - 2) + 4a = 60
=> 2 (2 + 2a) + 4a = 60
=> 4 + 4a + 4a = 60
=> 4 + 8a = 60 Subtract 4 from both side of the equation to isolate the term with the variable
=> 8a = 56 Divide both side of the equation by 8
=> a = 7

Now substitute that information to find out the number of tickets for children.
2c + 4a = 60
2c + 4(7) = 60
2c + 28 = 60 Subtract 28 from both side of the equation
2c = 32 Divide both side of the equation by 2
c = 16 • Hello,

Why is 4 + 4 x 2 is 12? If 4 plus 4 = 8, 8 times 2 is 16? • Agnes has 23 collectible stones, all of which are labradorite crystals or galena crystals. Labradorite crystals are worth \$20 each, while galena crystals are worth \$13 each. Agnes earns \$439 by selling her entire collection. How many stones of each type did she sell?

im stuck on this .
(1 vote) • This type of problem is pretty common on the SAT, and test to see if you can set up and solve a system of equations. What you want to do is group the information you have into two groups, from which you can create two equations. In this problem, you are given the total number of stones, the price per stone of each stone, and the total price of the collection. Based on the last sentence, you know that your variables should be the number of stones. Everything that talks about the prices seems related. If L is the number of Labradorite crystals and G is the number of galena crystals, you can represent the prices as this:
20L + 13G = 439
This is because multiplying the unit price per crystal by the amount of crystal will give you the money you would get for all the crystals of that type. Add this to the amount of money you would get for the other crystal type and you have the total.
We can set up another equation because we know how many crystals in total Agnes has, which is just x + y = 23.
Now you have the two equations set up, and it's time to solve them. This is a pretty necessary skill for the SAT, so if you don't know it already, I'd recommend you check out some videos on how the process works (https://www.khanacademy.org/math/algebra-basics/alg-basics-systems-of-equations). But, as always on SAT math, setting up this problem and figuring out how to do it is the actual hard part, and the actual doing it is more automatic.
You should end up getting 20 Labradorite crystals and 3 Galena crystals.