Ratio Problems: Practice

Multiply each ratio number by the common multiplier $k = 5$.

$2k = 2 \times 5 = 10, \quad 3k = 3 \times 5 = 15$

So the quantities are $10$ and $15$.

Add the two parts, combining like terms.

$4k + 3k = 7k$

The total is $7k$.

The total of the two parts is $3k + 5k = 8k$, and that equals $40$.

$3k + 5k = 8k = 40$

So the equation is $8k = 40$.

The parts total $3 + 5 = 8$, so $8k = 40$. Divide to find one part.

$k = \frac{40}{8} = 5$

The larger number is the $5$ term, so multiply $5$ by the part value $k = 5$.

$5k = 5 \times 5 = 25$

Oats is the $5$ term, so multiply $5$ by $k = 3$.

$5k = 5 \times 3 = 15$

The recipe uses $15$ cups of oats.

Cats is the $2$ term, so $2k = 6$. Divide to find one part.

$2k = 6 \implies k = 3$

Each ratio number is multiplied by the same part value $k$.

$1 : 2 : 3 \;\to\; k,\ 2k,\ 3k$

All three share one multiplier $k$.

Add the ratio numbers to count the parts.

$1 + 2 + 3 = 6$

There are $6$ equal parts in all.

There are $1 + 2 + 3 = 6$ parts, so $6k = 30$. Divide to find one part.

$6k = 30 \implies k = 5$

Equivalent ratios come from multiplying both parts of $2 : 3$ by the same number.

$2 : 3 = 4 : 6 = 6 : 9 = 10 : 15$

The pair $5 : 6$ is not a whole multiple of $2 : 3$, so it is not equivalent.

The larger quantity is the $6$ term, so multiply $6$ by $k = 4$.

$6k = 6 \times 4 = 24$