Question

3 choose yes or no to tell if you can use the equation to solve the problem below. ? - 23 = 61
yes no
61 - ? = 23
23 + 61 = ?
61 - 23 = ?
? - 61 = 23
4 there are 83 people on the subway. 47 people sit in seats. the rest of the people stand. how many people on the subway stand? write an addition equation and a subtraction equation that can be used to find the solution.
5 santo rides his bike 18 more miles than anwar. santo rides his bike 50 miles. how many miles does anwar ride his bike?
a 68
b 48
c 42
d 32
akiko chose a as the correct answer. how did akiko get her answer?
how are the numbers in the equation related?
how are addition and subtraction related?
if santo rides more miles than anwar, then who rides fewer miles?

Explanation:

Question 3

To determine if each equation can solve \(? - 23 = 61\) (where \(?\) is the minuend, 23 is the subtrahend, 61 is the difference):

• For \(61 -? = 23\): The original equation is \( \text{minuend} - \text{subtrahend} = \text{difference} \). Rearranging gives \( \text{minuend} = \text{subtrahend} + \text{difference} \), not \( \text{difference} - \text{minuend} = \text{subtrahend} \). So answer is No (B).
• For \(23 + 61 =?\): Using the relationship \( \text{minuend} = \text{subtrahend} + \text{difference} \), this works. So answer is Yes (C).
• For \(61 - 23 =?\): This calculates the difference of 61 and 23, not the minuend. So answer is No (F).
• For \(? - 61 = 23\): Rearranging gives \(? = 23 + 61\), which is the same as \(23 + 61 =?\), so this works. So answer is Yes (G).

Question 4

Let \( s \) = number of standing people. Total people = seated + standing:

• Addition equation: \( 47 + s = 83 \) (seated + standing = total).
• Subtraction equation: \( 83 - 47 = s \) (total - seated = standing).

Question 5

Let \( A \) = Anwar’s miles, \( S = 50 \) = Santo’s miles. Given \( S = A + 18 \), so \( A = S - 18 \).

• Step 1: Substitute \( S = 50 \): \( A = 50 - 18 \).
• Step 2: Calculate \( 50 - 18 = 32 \). So correct answer is D.

Akiko chose A (68) by adding 50 + 18 (mistakenly adding instead of subtracting), thinking Anwar rode more miles, but Santo rode more, so Anwar rode less (needs subtraction).

Answer:

s:

1. \(61 -? = 23\): B; \(23 + 61 =?\): C; \(61 - 23 =?\): F; \(? - 61 = 23\): G
2. Addition: \(47 + s = 83\); Subtraction: \(83 - 47 = s\)
3. Correct answer: D; Akiko added 50 + 18 (error).