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# Systems of linear equations word problems — Harder example

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

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• 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?

• 20 labradorite and 3 galena
because 20*20=400 and 3*13=39 so the total will be 439 which is exactly how much Agnes made
• 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!
• Don't overlook "the remaining adults brought 2 children EACH." So, it's children per adult regardless; singles or couples.
• 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?