Eileen had 3 times as much money as Jason at first. After Jason spent $290 and Eileen’s father gave her $446 more, Eileen had 7 times as much as what Jason had in the end. How much money did Jason have at first?
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Question
Answer
BigDevil
Sorry…no time to draw a nice model now.
At first
E -> [ u + 290 ][ u + 290 ][ u + 290 ]
J -> [ u + 290 ]
Change
E -> + $446
J -> – $290
After
E -> [ u ][ u ][ u ][ u ][ u ][ u ][ u ]
J -> [ u ]
But E in the end is also [ u + 290 ][ u + 290 ][ u + 290 ][ $446 ]
7u = (u + 290) + (u + 290) + (u + 290) + 446
7u = 3u + 1316
4u = 1316
u = 329
At first, Jason had (u + 290) = 329 + 290 = $619
SAHMom
Hi BigDevil, found a little time and hope my model is acceptable. 🙂
For general note here: By P5, kids should know how to draw the first 2 sets “Before” and “After” well. It is the analysis part (circled above) that some kids need more practice with. So depending on the competency level the child is at, he may need to work on model drawing or analysis part or both.
But then again, some kids or parents give up model drawing totally and go for the algebra method. To me, it is a pity to give heuristics a complete miss and not enjoy the process. Most of us (parents) here had never touched model drawing in our old school and we learn anyway.
SAHMom
Hi BigDevil, found a little time and hope my model is acceptable. 🙂
For general note here: By P5, kids should know how to draw the first 2 sets “Before” and “After” well. It is the analysis part (circled above) that some kids need more practice with. So depending on the competency level the child is at, he may need to work on model drawing or analysis part or both.
But then again, some kids or parents give up model drawing totally and go for the algebra method. To me, it is a pity to give heuristics a complete miss and not enjoy the process. Most of us (parents) here had never touched model drawing in our old school and we learn anyway.
BigDevil
Of course it is acceptable. 🙂
There is no right or wrong way of drawing a model. A model is simply a visual aid to help solve the problem. As long as the kids can understand and use it to solve the problem, it is a good model. 😀
alfretztay
At first —
Eileen : 1u + 1u + 1u = 3u
Jason : 1u
After —
Eileen : 3u + 446
Jason : 1u – 290
(1u – 290) x 7 = 7u – 2030 ——-3u + 446
7u – 3u = 4u ——- 446 + 2030 = 2476
1u ——- 2476/4 = 619
Ans : $619.