Devin tried to evaluate 7\times 5{,}0707×5,0707, times, 5, comma, 070 step by step.
\phantom{=}\greend7\times\blued{5{, }070}=7×5,070empty space, start color #1fab54, 7, end color #1fab54, times, start color #11accd, 5, comma, 070, end color #11accd
{\text{step } 1}step 1start text, s, t, e, p, space, end text, 1 =\greend7\times (\blued{5{,}000} + \blued{70} )=7×(5,000+70)equals, start color #1fab54, 7, end color #1fab54, times, left parenthesis, start color #11accd, 5, comma, 000, end color #11accd, plus, start color #11accd, 70, end color #11accd, right parenthesis
{\text{step } 2}step 2start text, s, t, e, p, space, end text, 2 =(\greend7 \times \blued{5{,}000}) + (\greend7 \times \blued{70})=(7×5,000)+(7×70)equals, left parenthesis, start color #1fab54, 7, end color #1fab54, times, start color #11accd, 5, comma, 000, end color #11accd, right parenthesis, plus, left parenthesis, start color #1fab54, 7, end color #1fab54, times, start color #11accd, 70, end color #11accd, right parenthesis
{\text{step } 3}step 3start text, s, t, e, p, space, end text, 3 =35{,}000 + 490=35,000+490equals, 35, comma, 000, plus, 490
{\text{step } 4}step 4start text, s, t, e, p, space, end text, 4 =39{,}900=39,900equals, 39, comma, 900
find devin's mistake.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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