Question

2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.

Answer 1

Melties charges $0.45 per ounce for frozen yogurt and $2.83 for the cone. This was determined by creating a system of linear equations from two separate purchases and then solving for the cost per ounce and the cone cost.

Step-by-step explanation:

To determine how much Melties charges per ounce of frozen yogurt and for the cone, we can set up two equations based on the purchases of Al and Beth:

Let x be the cost per ounce of the frozen yogurt, and y be the cost of the cone.

For Al's purchase: 3.6x + y = 4.47

For Beth's purchase: 4.8x + y = 5.01

Now, we have a system of linear equations that we can solve. Subtraction one equation from the other eliminates y and gives us the cost per ounce x:

(4.8x + y) - (3.6x + y) = 5.01 - 4.47

1.2x = 0.54 which simplifies to x = 0.54 / 1.2

Therefore, x = $0.45 per ounce for the frozen yogurt.

Substitute the value of x into one of the original equations:

3.6(0.45) + y = 4.47

y = 4.47 - (3.6 \(*\) 0.45)

After the calculation, y = $2.83 for the cone.

Melties charges $0.45 per ounce for frozen yogurt and $2.83 for a cone.

Answer 2

2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.​

Let

x ------> the number of ounces of frozen yogurt

y ------> the total charge

we have the ordered pairs

(3.6,4.47) and (4.8,5.01)

step 1

Find the slope pr unit rate

m=(5.01-4.47)/(4.8-3.6)

m=$0.45 per ounce

step 2

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=0.45

(x1,y1)=(3.6,4.47)

substitute

y-4.47=0.45(x-3.6)

convert to slope intercept form

y-4.47=0.45x-1.62

y=0.45x+2.85

In this problem, the y-intercept or initial value correspond to the charge for the cone

so

$2.85