High School

6. Write an equation for the following and then solve:
The product of a number and 6 is 48. Find the number.
The number is ________.

7. Write an equation for the following and then solve:
A number decreased by 9 is -9. Find the number.
The number is ________.

8. Write an equation for the following and then solve:
y divided by 17 is equal to -14. Find y.
y = _______.

9. Write an equation for the following and then solve:
The product of w and 19 is equal to 285. Find w.
w = _______.

10. Write an equation for the following and then solve:
The product of q and 8.4 is equal to 100.8. Find q.
q = ________.

11. Write an equation for the following and then solve:
The sum of x and 7 is equal to -41. Find x.
x = ________.

12. A change purse contains an equal number of pennies, nickels, and dimes. The total value of the coins is 528 cents. How many coins of each type does the purse contain?
Number of pennies = _________.

13. A cash register contains only five dollar and ten dollar bills. It contains twice as many fives as tens, and the total amount of money in the cash register is 560 dollars. How many tens are in the cash register?
Answer = _________.

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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