3 quarters, 1 dime, 2 nickels, and 1 penny

by bahzbsbaEVYHIGDYSVUW
(NY)

Howard has 3 quarters, 1 dime, 2 nickels, and 1 penny. Felicia has 1 quarter, 5 nickels, and 3 pennies. Together, the friends go to the store to buy colored pencils for school. Howard has enough money to buy 5 pencils but not enough for 6 pencils. Felicia has enough for 3 pencils but enough for 4. How much does a pencil cost.

Comments for 3 quarters, 1 dime, 2 nickels, and 1 penny

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Jan 08, 2012

Word Problems
by: Staff

Question:

by bahzbsbaEVYHIGDYSVUW
(NY)

Howard has 3 quarters, 1 dime, 2 nickels, and 1 penny. Felicia has 1 quarter, 5 nickels, and 3 pennies. Together, the friends go to the store to buy colored pencils for school. Howard has enough money to buy 5 pencils but not enough for 6 pencils. Felicia has enough for 3 pencils but enough for 4. How much does a pencil cost?

Answer:

Howard has 3 quarters, 1 dime, 2 nickels, and 1 penny.

H = 3*(.25) + 1*(.10) + 2*(.05) + 1*(.01)

H = 0.96

Felicia has 1 quarter, 5 nickels, and 3 pennies.

F = 1*(.25) + 0*(.10) + 5*(.05) + 3*(.01)

F = 0.53

Together, the friends go to the store to buy colored pencils for school.

Howard has enough money to buy 5 pencils but not enough for 6 pencils.

H = 0.96

5P ≤ H < 6P

5P ≤ 0.96 < 6P

Solve each part of the inequality separately

5P ≤ 0.96

Divide each side of the inequality by 5

5P/5 ≤ 0.96/5

P*(5/5) ≤ 0.96/5

P*(1) ≤ 0.96/5

P ≤ 0.96/5

P ≤ 0.192

0.96 < 6P

Divide each side of the inequality by 6

0.96/6 < 6P/6

0.96/6 < P*(6/6)

0.96/6 < P*(1)

0.96/6 < P

0.16 < P

Harold: 0.16 < P ≤ 0.192
(for Harold to buy 5 pencils with $0.96, but not have enough money to buy 6 pencils, the cost of each pencil must be greater than $0.16 and less than or equal to $0.192)

Felicia has enough for 3 pencils but enough for 4.

F = 0.53

3P ≤ F < 4P

3P ≤ 0.53 < 4P

Solve each part of the inequality separately

3P ≤ 0.53

Divide each side of the inequality by 3

3P/3 ≤ 0.53/3

P*(3/3) ≤ 0.53/3

P*(1) ≤ 0.53/3

P ≤ 0.53/3

P ≤ 0.176667

0.53 < 4P

Divide each side of the inequality by 4

0.53/4 < 4P/4

0.53/4 < P*(4/4)

0.53/4 < P*(1)

0.53/4 < P

0.1325 < P

Felicia: 0.1325 < P ≤ 0.176667
(for Felicia to buy 3 pencils with $0.53, but not have enough money to buy 4 pencils, the cost of each pencil must be greater than $0.1325 and less than or equal to $0.176667)

How much does a pencil cost?

Harold: 0.16 < P ≤ 0.192

Felicia: 0.1325 < P ≤ 0.176667

To meet the criteria for both people, pick the most restrictive price constraints:

0.16 < P ≤ 0.176667

>>>>>>>>>>>>>>>>>>>>>The FINAL ANSWER: the cost of each pencil must be greater than $0.16 and less than or equal to $0.176667

Thanks for writing.
Staff
www.solving-math-problems.com

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3 quarters, 1 dime, 2 nickels, and 1 penny

Comments for 3 quarters, 1 dime, 2 nickels, and 1 penny