Question

you buy 6 health bars and 2 health drinks for $22. Your friend buys 5 health bars and 3 health drinks for $21. What is the cost of each health bar? of each health drink?

Answer 1

Step-by-step explanation:

Let x = the unknown cost of a single hot dog and y = the unknown cost of a single soft drink. We have two unknowns so we need two equations to find them.

Equation 1 - 10 hot dogs and 5 soft drinks cost $35; that is 10x + 5y = 35

Equation 2 - 7 hot dogs and 4 soft drinks cost $25.25; that is 7x + 4y = 25.25

First let's re-write equation 1 to solve for y:

10x + 5y = 35

5y = 35 - 10x (subtract 10x from both sides)

y = 7 - 2x (divide both sides by 5)

Next, let's substitute 7 - 2x for y in equation 2:

7x + 4y = 25.25

7x + 4(7-2x) = 25.25

7x + 28 - 8x = 25.25

-x + 28 = 25.25

x - 28 = -25.25

Solve for x, the cost of a single hot dog. Once you have that, use y = 7 - 2x to find the cost of a single soft drink.

Answer 2

Answer:

Cost of 1 health bar = $3

Cost of 1 health drink = $2

Step-by-step explanation:

Given:

Cost of 6 health bars and 2 health drinks = $22

Cost of 5 health bars and 3 health drinks = $21

Find:

Cost of 1 health bar = ?

Cost of 1 health drink = ?

Solution:

Step 1:

Let the cost of 1 health bar = $x$

Let the cost of 1 health drink = $y$

Step 2:

Cost of 6 health bars and 2 health drinks = $22

That is,

$6x+2y=22$    ---------> (1)

Cost of 5 health bars and 3 health drinks = $21

That is,

$5x+3y=21$     ---------> (2)

Step 3:

Now, make equal coefficients to either $x$ or $y$

Let us make the coefficient of $y$ equal,

Eqn. (1) × 3

⇒ $3 \times (6x+2y=22)$

⇒ $18x+6y=66$    ----------> (3)

Eqn. (2) × 2

⇒ $2 \times (5x+3y=21)$

⇒ $10x+6y=42$    ----------> (4)

Step 4:

Eqn.(3) - Eqn.(4)

$18x+6y=66\ \ (-)\\10x+6y=42$

⇒ $8x=24$

⇒ $x = \frac{24}{8}$

⇒ $x=3$

Therefore, cost of 1 health bar = $3

Step 5:

Substitute $x=3$ in Eqn. (1),

$6x+2y=22$

⇒ $(6 \times 3) +2y =22$

⇒ $18+2y=22$

⇒ $2y=22-18$

⇒ $2y=4$

⇒ $y=2$

Therefore, cost of 1 health drink = $2

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