Answers:
- a) x+y = 70
- b) The graph is shown below. The lines intersect at (20, 50) meaning that she has 20 quarters and 50 dimes.
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Explanation:
a)
x = number of quarters
y = number of dimes
x+y = number of dimes and quarters
x+y = 70 coins total
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b)
Use a graphing tool like Desmos or Geogebra to plot each linear equation on the same xy grid. I'm using Geogebra to get what is shown below.
The red line 25x+10y = 1000 goes through (0,100) and (40,0)
The blue line x+y = 70 goes through (0,70) and (70,0)
The two lines intersect at (x,y) = (20,50)
This means x = 20 and y = 50 pair up together.
Kateri has 20 quarters and 50 dimes
- 20 quarters = 20*25 = 500 cents = 500/100 = $5
- 50 dimes = 50*10 = 500 cents = 500/100 = $5
Total value = $5 + $5 = $10
Also note that 20 quarters + 50 dimes = 70 coins total
Both conditions have been confirmed.
