Von's arcade uses 3 different colored tokens for its game machines. For 500, you can purchase any of the following combinations of tokens: 8 gold, 18 silver, and 7 bronze tokens; 8 gold, 14 silver, and 13 bronze tokens; or 16 gold, 6 silver, and 9 bronze tokens. What is the monetary value of each token?
There are three prime numbers whose sum is 67. Twice the smallest number is 3 more than the middle number. The difference of the largest and the middle number is 8. What are these prime numbers?
Jen is the top 1 of her class during the second quarter. Her average grade in her Algebra, English, and Science subjects is 93. Her average grade in English and Science is eqaul to her grade in Algebra, while her average grade in Algebra and English is 3 less than her grade in Science. What are her grades in each of the three subjects?
8g+18s+7b = 500
8g+14s+13b = 500
16g+6s+9b = 500
gold=20
silver=15
bronze=10
x+y+z = 67
2x = y+3
z-y = 8
The numbers are 13,23,31
(a+e+s)/3 = 93
(e+s)/2 = a
(a+e)/2 = s-3
Her grades are 93,91,95
To solve the first question about Von's arcade, we can set up a system of equations. Let's assume the monetary value of a gold token is x dollars, the value of a silver token is y dollars, and the value of a bronze token is z dollars.
From the given information, we know the following equations:
8x + 18y + 7z = 500
8x + 14y + 13z = 500
16x + 6y + 9z = 500
We can solve this system of equations to find the values of x, y, and z, which represent the monetary value of each token.
To solve the second question about three prime numbers whose sum is 67, we can use logic and trial and error. We know that the sum of three prime numbers is 67, so the smallest prime number must be less than 22 (since 22 + 22 + 23 = 67). We also know that twice the smallest number is 3 more than the middle number, and the difference between the largest and middle number is 8.
By trying different combinations of prime numbers that satisfy these conditions, we can find the three prime numbers that add up to 67.
To solve the third question about Jen's grades, we can set up additional equations based on the given information.
Let A be Jen's grade in Algebra, E be her grade in English, and S be her grade in Science.
From the given information, we know the following equations:
(A + E + S) / 3 = 93
(E + S) / 2 = A
(A + E) = S - 3
We can solve this system of equations to find Jen's grades in each subject.