4. John and Peter made hot dogs to earn money for their cricket tour. John is a faster worker and made 3 hot dogs for every 2 that Peter made. How many did each of them make if 280 hot dogs were made in total?

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UpStudy AI · Accepted Answer

Let $$ J $$ be the number of hot dogs John made and $$ P $$ be the number of hot dogs Peter made. We are given that

$$
\frac{J}{P} = \frac{3}{2} \quad \text{and} \quad J + P = 280.
$$

This means we can express John's production as

$$
J = \frac{3}{2}P.
$$

Substitute $$ J = \frac{3}{2}P $$ into the total:

$$
\frac{3}{2}P + P = 280.
$$

Combine like terms by expressing $$ P $$ as $$ \frac{2}{2}P $$:

$$
\frac{3}{2}P + \frac{2}{2}P = \frac{5}{2}P = 280.
$$

Multiply both sides by $$ \frac{2}{5} $$ to solve for $$ P $$:

$$
P = 280 \times \frac{2}{5} = \frac{560}{5} = 112.
$$

To find $$ J $$, substitute $$ P = 112 $$ back into $$ J = \frac{3}{2}P $$:

$$
J = \frac{3}{2} \times 112 = 3 \times 56 = 168.
$$

Thus, John made $$ 168 $$ hot dogs and Peter made $$ 112 $$ hot dogs.
John made 168 hot dogs and Peter made 112 hot dogs.

4. John and Peter made hot dogs to earn money for their cricket tour. John is a faster worker and made 3 hot dogs for every 2 that Peter made. How many did each of them make if 280 hot dogs were made in total?

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