Question

three brothers are saving for a special trip. the ratio of oscar’s savings to nick’s savings is 8:3 and the ratio of nick’s savings to liam’s savings is 3:5. together all 3 brothers have saved $64. how much has each boy saved? answer questions 3–4.

1. complete the table.

you can draw 3 bar diagrams. oscar’s is 8 squares long, nick’s is 3 squares long, and liam’s is 5 squares long. then, use the diagrams to show $64. (type whole numbers.)

oscar’s savings	$8	$16	$24	$32
liam’s savings	$5	$10	$15	$20

describe how the table can be used to solve the problem. choose the correct answer below.

a. the table shows equivalent ratios that relate each brother’s savings. extend the table until one of the entries in the last column is $64. that column shows how much each boy has saved.

b. the table shows equivalent ratios that relate each brother’s savings. add the amounts in each row to find the total saved. the numbers in the last row add to $64, so that row shows how much each boy has saved.

c. the table shows equivalent ratios that relate each brother’s savings. add the amounts in each column to find the total saved. the numbers in the last column add to $64, so that column shows how much each boy has saved.

d. the table shows equivalent ratios that relate each brother’s savings. extend the table until one of the entries in the last row is $64. that row shows how much each boy has saved.

Explanation:

Step1: Unify the ratio terms

First, combine the two given ratios to get the ratio of Oscar's savings to Nick's to Liam's.
Oscar:Nick = 8:3, Nick:Liam = 3:5. So Oscar:Nick:Liam = 8:3:5.
Let the savings be $8x$, $3x$, and $5x$ respectively.

Step2: Set up total savings equation

The total savings of the three boys is $64.
$8x + 3x + 5x = 64$
$\implies 16x = 64$

Step3: Solve for x

Calculate the value of $x$.
$x = \frac{64}{16} = 4$

Step4: Calculate each boy's savings

Substitute $x=4$ into the expressions for each boy's savings.
Oscar: $8x = 8\times4 = 32$
Nick: $3x = 3\times4 = 12$
Liam: $5x = 5\times4 = 20$

Step5: Verify the table usage

The table provides equivalent ratios for each boy's savings. We find the row where the sum of the three values equals $64$. The row with $\$32$, $\$12$, $\$20$ sums to $32+12+20=64$, which matches the total savings.

Answer:

Question 3:

Oscar saved $\$32$, Nick saved $\$12$, Liam saved $\$20$.

Question 4:

C. The table shows equivalent ratios that relate each brother's savings. Add the amounts in each column to find the total saved. The numbers in the last column add to $64, so that column shows how much each boy has saved.