James wants to compete in the international speed texting competition next year where participants compete on text speed and accuracy. James

Question

James wants to compete in the international speed texting competition next year where participants compete on text speed and accuracy. James’s current text speed is 2 characters per second. James has found that his texting speed increases at a rate of 1⁄2 a character per second for each month that he practices.
1. a. What is James’s new texting speed if he practices for only 1 month? __________
b. What is James’s new texting speed if he practices for 2 months? ____________
c. What is his new texting speed if he practices for 3 months? _____________
d. Write an algebraic equation that gives James’s texting speed s for m months of
practice.

2. a. Solve the equation from question 1d to determine how many months of practice it will
take before James’s texting speed reaches 8 characters per second.
b. Explain the steps to solve your equation from question 2a.

3. a. If Lydia wants to text at least 8 characters per second, like James, then the equation
10r + 4 = 8 could be used to model this situation. Solve this equation for r.
b. Explain what the variable r represents in the equation given in question 3.

4. Consider the equation 8x + 5 = 37. Write a real-life scenario that this equation could model.

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2 weeks 2021-09-13T21:48:59+00:00 1 Answer 0

1. 1a 2.5 characters per second

1b 3 characters per second

1c 3.5 characters per second

1d s = 2 + 0.5m

2a 8 = 2 +0.5m

6=0.5 m

m=12

2b the final speed James wants is 8 cps. sub that in for s. we want to know m. first, subtract 2 from both sides to get 6. then, divide by 0.5, which is 1/2 as a fraction. In order to divide a number by a fraction, you need to invert the fraction and switch operations from division to multiplication. It becomes 2/1 * 6 = 12.

3a 10 r +4 = 8

10r =4

r =4/10=2/5

3b. In this equation, r could be the increase in amount of characters that Lydia can type per second.

4. John buys a small tree that is 5 inches tall. Each month, this tree grows 8 inches. How long will it take for the tree to reach 37 inches in height?

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