Question

1. a construction company is moving cinder blocks. the table shows the total weight in pounds, w, of n cinder blocks. which equation could represent the total weight, in pounds, for n cinder blocks?

number of cinder blocks | total weight in pounds
0 | 0
1 | 40
2 | 80
3 | 120

1. han is collecting dimes and quarters in a jar. he has collected $25.25 so far. the relationship between the numbers of dimes and quarters, and the amount of money in dollars is represented by the equation 0.10d + 0.25q = 25.25.

select all the values (d, q) that are solutions to the equation.
a. (1.5, 95)
b. (25, 91)
c. (132, 48)
d. (195, 23)
e. (255, 1)

Explanation:

Problem 1

Step1: Identify the relationship

From the table, when \( n = 0 \), \( W = 0 \); \( n = 1 \), \( W = 40 \); \( n = 2 \), \( W = 80 \); \( n = 3 \), \( W = 120 \). The weight increases by 40 for each additional block, so it's a proportional relationship.

Step2: Form the equation

The general form for a proportional relationship is \( W = kn \), where \( k \) is the constant of proportionality. From \( n = 1 \), \( W = 40 \), so \( k = 40 \). Thus, the equation is \( W = 40n \).

To check if a pair \((d, q)\) is a solution, substitute \( d \) and \( q \) into the equation \( 0.10d + 0.25q = 25.25 \) and see if it holds true.

Step1: Check Option A \((1.5, 95)\)

\( d = 1.5 \) (number of dimes can't be a non - integer in this context, but mathematically: \( 0.10\times1.5+0.25\times95 = 0.15 + 23.75=23.9
eq25.25\)), so not a solution.

Step2: Check Option B \((25, 91)\)

\( 0.10\times25+0.25\times91=2.5 + 22.75 = 25.25\), so it is a solution.

Step3: Check Option C \((132, 49)\)

\( 0.10\times132+0.25\times49 = 13.2+12.25 = 25.45
eq25.25\), so not a solution.

Step4: Check Option D \((195, 23)\)

\( 0.10\times195+0.25\times23=19.5 + 5.75 = 25.25\), so it is a solution.

Step5: Check Option E \((255, 1)\)

\( 0.10\times255+0.25\times1=25.5 + 0.25 = 25.75
eq25.25\), so not a solution.

Answer:

\( W = 40n \)

Problem 2