Answer:
Part 1)
A) [tex]3:6[/tex] and [tex]5:10[/tex]
B) [tex]4/12[/tex] and [tex]6/18[/tex]
Part 2) Option B. [tex]P=28[/tex]
Part 3) Option A. [tex]1[/tex]
Step-by-step explanation:
Part 1) Verify each case
case A) [tex]3:6[/tex] and [tex]5:10[/tex]
[tex]\frac{3}{6}=\frac{5}{10}[/tex]
Multiply in cross and then compare
[tex]3*10=6*5[/tex]
[tex]30=30[/tex] -----> is true
therefore
Is a true proportion
case B) [tex]4/12[/tex] and [tex]6/18[/tex]
[tex]\frac{4}{12}=\frac{6}{18}[/tex]
Multiply in cross and then compare
[tex]4*18=12*6[/tex]
[tex]72=72[/tex] -----> is true
therefore
Is a true proportion
case C) [tex]20/5[/tex] and [tex]10/3[/tex]
[tex]\frac{20}{5}=\frac{10}{3}[/tex]
Multiply in cross and then compare
[tex]20*3=5*10[/tex]
[tex]60=50[/tex] -----> is not true
therefore
Is not a true proportion
case D) [tex]25:36[/tex] and [tex]8:9[/tex]
[tex]\frac{25}{36}=\frac{8}{9}[/tex]
Multiply in cross and then compare
[tex]25*9=36*8[/tex]
[tex]225=288[/tex] -----> is not true
therefore
Is not a true proportion
Part 2) Solve the proportion [tex]\frac{42}{15}=\frac{P}{10}[/tex]
Multiply in cross and solve for P
[tex]42*10=15*P[/tex]
[tex]P=420/15=28[/tex]
Part 3) Which is the better buy?
1. 5 oranges for $1.60.
2. 7 oranges for $2.45
Find the units rates
First case
[tex]\frac{1.60}{5}=0.32 \frac{\$}{orange}[/tex]
Second case
[tex]\frac{2.45}{7}=0.35 \frac{\$}{orange}[/tex]
The better buy is the first case
because
[tex]0.32 \frac{\$}{orange}< 0.35 \frac{\$}{orange}[/tex]
