Guess and Check Homework

Note: These problems all come from the Math Olympiad competitions indicated.

2012 algebra problem #3:
1). There were 36 heads and 104 legs in a group of horses and riders. How many riders were in the group? (Make sure the number of horses and riders adds to 36)

Guess #	# Horses	# riders	total heads	total legs
1	9	27	36	88
2
3
4
5

Answer this question first:
This first guess results in 88 legs and I need 104 legs. Therefore I need to increase the number of _______ and decrease the number of _____.

Answer: ___________ riders.

2013 algebra problem #5:
2). Mrs. Severson keeps a jar with pennies and dimes in her classroom as a tool for teaching place value to her young students. Jori reaches in and pulls out a handful of coins and counts them. She has 43 coins. Tom computes and finds out the handful is worth 88 cents. How many are pennies?

Guess	Number of pennies	Number of dimes	Total
1	42	1	52 cents

Answer this question first:
The first guess results in 52 cents and I need 88 cents, therefore I must increase the number of ______ and decrease the number of _______.

Answer: ______ pennies.

2017 algebra problem #3:
3). A pile of 28 coins is worth $4.80. There are only quarters and nickels in the pile. How many quarters are there?

Guess #	# quarters	# nickels	Total $
1	15	13	$4.40

Answer this question first:
The first guess results in a pile worth $4.40 and I want $4.80, therefore I must increase the number of _______ and decrease the number of __________.

Answer: ______ quarters.