Patterns & Reasoning

Problem

Fill a table and complete a line graph from clues

A line graph of picture frames made each month shows April = 280, May = 380, June = 180; July and August are blank. July is 80 more than June, and July + August together is 640. I must find the July and August counts to complete the graph.
Picture Frames Made 0 100 200 300 400 (frames) 4 5 6 7 8 Month
Measurement & data
Your answer
How to solve
Strategy Identify Subproblems — I solve in order from what I can already know: first July (June plus 80), then August (the 640 total minus July). Each is a one-step subproblem, and finding August uses the total backwards.
1STEP 1

Find July

July is 80 more than June, and June is 180, so July = 180 + 80 = 260.

180 + 80 = 260
2STEP 2

Find August

July and August together make 640, so August = 640 - 260 = 380.

640 - 260 = 380
3STEP 3

Plot the points

On the graph (each square = 20), July 260 sits 3 squares above 200, August 380 sits 4 squares above 300; join the points in order.

260 = 200 + 3× 20, 380 = 300 + 4× 20
Answer
July = 260 frames, August = 380 frames
Check the clues: July 260 is indeed 80 more than June 180, and July 260 + August 380 = 640 as required. Both values land neatly on grid lines (260 and 380 are multiples of 20), so the plotted points are valid.
Takeaway

Fill in what you can figure out first, then use the total to get the rest - then just plot!

  • Find July
  • Find August
  • Plot the points
Where next?
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