Q18. - Algebra 1

Question

The table shows how many canned goods were collected during the first day of a charity food drive.

 

Food Drive day 1 Results
Class	Number Collected
${\mathbf{10}}^{\mathbf{t}\mathbf{h}\mathbf{ }}$graders	78
${\mathbf{11}}^{\mathbf{t}\mathbf{h}}$ graders	80
${\mathbf{12}}^{\mathbf{t}\mathbf{h}}$ graders	92

 

a. Estimate how many canned goods will be collected during the 5-day food drive. Explain your answer.

 

b. Is this estimate a reasonable expectation? Explain.

Step-by-Step Solution

Answer

a. 1250 canned goods will be collected during 5-day food drive.

b. The estimation is not a reasonable expectation.

Part a Step 1. Estimate the total number of canned goods collected in 1 day.

From the table given below, calculate the total number of canned goods collected in 1 day.

 

Food Drive day 1 Results
Class	Number Collected
${\mathbf{10}}^{\mathbf{t}\mathbf{h}}$ graders	78
${\mathbf{11}}^{\mathbf{t}\mathbf{h}}$ graders	80
${\mathbf{12}}^{\mathbf{t}\mathbf{h}}$ graders	92

$\begin{array}{c}\text{Total number of canned goods collected in 1 days=78+80+92}\\ \text{=250}\end{array}$

Part a Step 2. Make the assumption.

As there is no information regarding the rate at which the canned goods are collected in each days, assume that same number of canned goods are collected by every graders in each 5 days. That is everyday 250 canned goods are collected.

Part a Step 3. Estimate the total number of canned goods collected in 5 days.

The total number of canned goods collected in 5 days is calculated as follows

$\begin{array}{c}\text{Total\hspace{0.17em}\hspace{0.17em}number\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}canned\hspace{0.17em}\hspace{0.17em}goods\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}collected\hspace{0.17em}\hspace{0.17em}in\hspace{0.17em}\hspace{0.17em}5\hspace{0.17em}\hspace{0.17em}days=5}\times \text{250}\\ \text{=1250}\end{array}$                                                                   

1250 canned goods will be collected during the 5-day food drive.

Part bStep 1. Write the estimated value from previous steps.

The estimated value of canned goods collected in 5 days is 1250.

Part b Step 2. Determine whether the assumption made in the step 2 of part ( a ) is correct.

The assumption made was as ideal case. There might have been a change in the rate at which the canned goods are collected everyday by the graders. It might have been less then or more than the first day.

Part b Step 3. State the conclusion.

As the rate is not given in the case. Therefore, the number of canned goods collected may not be the 5 times of the total numbers collected in day 1.

Hence, the estimation is not a reasonable expectations.