Answer :
Final Answer:
The solutions to the given equations are as follows:
6. The number is 8.
7. The number is 0.
8. y = -238.
9. w = 15.
10. q = 12.
11. x = -48.
12. Number of pennies = 88.
13. Number of tens = 20.
Explanation:
6. "The product of a number and 6 is 48" translates to the equation 6n = 48, where n represents the number. Solving for n gives n = 8.
7. "A number decreased by 9 is -9" becomes the linear equation n - 9 = -9. Solving for n yields n = 0.
8. "y divided by 17 is equal to -14" is represented by the equation y/17 = -14. Solving for y gives y = -238.
9. "The product of w and 19 is equal to 285" translates to the equation 19w = 285. Solving for w results in w = 15.
10. "The product of q and 8.4 is equal to 100.8" becomes the equation 8.4q = 100.8. Solving for q gives q = 12.
11. "The sum of x and 7 is equal to -41" is represented by the equation x + 7 = -41. Solving for x yields x = -48.
12. "A change purse contains an equal number of pennies, nickels, and dimes" gives the equation p + n + d = 528, where p, n, and d represent the number of pennies, nickels, and dimes, respectively. Since they're equal, we have 3p = 528, and solving for p results in p = 88.
13. "A cash register contains only five dollar and ten dollar bills" leads to the equation 5f + 10t = 560, where f and t represent the number of five dollar and ten dollar bills, respectively.
Given that there are twice as many fives as tens, we have f = 2t. Substituting this into the equation gives 5(2t) + 10t = 560, which simplifies to 20t = 560. Solving for t gives t = 20.
These solutions demonstrate solving equations and determining unknown values based on given conditions.
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