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.

Answer 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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