Tavon has a gift card for $110 that loses $2.50 for each​ 30-day period it is not used. He has another gift card for $90 that loses $2 for each​ 30-day period it is not used.
a. Write and solve an equation for the number of​ 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal​ value?

Tavon Has A Gift Card For $110 That Loses $2.50 For Each 30-day Period It Is Not Used. He Has Another

Answers

Answer 1

30 day period

The first equation is 50 - 2x (because you start with $50 and subtract 2 for each 30 day period)

The second equation is 40-1.5x

Set them equal to each other:  50 - 2x = 40 - 1.5x

Solve for x:

50 - 2x = 40 - 1.5

  +2x   +2x

50 = 40 + 0.5 x

-40   -40

-------------------

10 = 0.5 x

20 = x

So there will be 20 30-day periods until the cards will be equal in value.

Check:  After 20 periods, 50 - 2(20) = $10 left

40 - 1.5(20) = also $10 left

Answer 2

The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal​ value, will be $10.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let x be the number of days and y be the value of the card.

Tavon has a gift card for $110 that loses $2.50 for each​ 30-day period it is not used. He has another gift card for $90 that loses $2 for each​ 30-day period it is not used. Then the equations will be

y = 110 - 2.5x    ...1

y = 90 - 2x       ...2

From equations 1 and 2, we have

110 - 2.5x = 90 - 2x

20 = 0.5x

x = 40

And the value of y will be

y = 110 - 2.5(40)

y = 110 - 100

y = $10

The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal​ value, will be $10.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2


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Hi there!

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I hope this helps!

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The students must make use of varying string lengths in his experiment in other to make string length the independent quantity.

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9514 1404 393

Answer:

  -2 7/8

Step-by-step explanation:

The usual recommendation is to convert the mixed numbers to improper fractions before multiplying.

  [tex]-2\dfrac{5}{9}\times1\dfrac{1}{8}=-\dfrac{9\cdot2+5}{9}\times\dfrac{8\cdot1+1}{8}\\\\=-\dfrac{23\cdot9}{9\cdot8}=-\dfrac{23}{8}=\boxed{-2\dfrac{7}{8}}[/tex]

__

Note the factors of 9 cancel in the first expression on the last line, leaving -23/8.

Answer:

[tex]\frac{23}{8}=2\frac{7}{8}[/tex]

Step-by-step explanation:

[tex]-2\frac{5}{9}\times \:1\frac{1}{8}[/tex]

Step 1: Convert into an improper fraction

[tex]2\frac{5}{9}=\frac{2\times 9+5}{9}\\\\=\frac{23}{9}[/tex]

[tex]-\frac{23}{9}\times \:1\frac{1}{8}[/tex]

[tex]1\frac{1}{8}=\frac{1\times 8+1}{8}\\\\=\frac{9}{8}[/tex]

[tex]-\frac{23}{9}\times \frac{9}{8}[/tex]

Step 2: Cross-cancel 9

[tex]=-\frac{23}{8}[/tex]

Step 3: Convert to an improper fraction

[tex]\frac{23}{8}=2\frac{7}{8}\\\\2\frac{7}{8}[/tex]

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