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October 7th, 2019, 11:41 AM   #1
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Question Help turning word problems into equations please...

Hello, my class has just started exploring rational equations. I have no problem solving the equations on their own but when I need to convert information into these equations I can confuse myself. If anyone can help me with turning these two problems into rational equations, I'd be really grateful!

1. A school purchases a load of t-shirts with their emblem for \$450.
They then put aside two t-shirts, and sell the rest for \$560, at \$10 per shirt.
How many shirts were in the initial shipment?

2. Two boys are walking for 30km. Boy-A walks at a pace 1.4km/h faster then Boy-B.
Boy-A stops during his walk to talk with a friend for 20min, however, he still completes the 30km walk 2hrs before Boy-B.
How long did they each take to complete the walk?

Thank you for your help !

Last edited by SimpleMinded; October 7th, 2019 at 12:26 PM.
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October 7th, 2019, 11:58 AM   #2
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1. Let N be the number of t-shirts ordered. You are told two things:
(a) A school purchases a load of t-shirts with their emblem for \$450.
Equation: $Buying~cost = \$ 450$
Implied equation: $\$450 = N\cdot (buying~cost~per~shirt)$
(b) Then, they put aside two t-shirts and sell the rest for \$560, \$10 per shirt.
Equation: $(N-2~shirts)\cdot (\$10/shirt) = \$560$

(a) is irrelevant, (b) allows you to find N.

2. "Two boys are walking for 30km." Let $L = 30~km$ be the distance travelled.
"Boy-A walks at a pace 1.4km/h faster then Boy-B." Let $V_A$ and $V_B$ be their respective speeds. Then $V_A = V_B + 1.4~ km/hr$.
"Boy-A stops during his walk to talk with a friend for 20min" Let $t_A$ and $t_B$ be the time Boy A takes and the time Boy B takes to walk the 30 km. Time is length/speed, so $\displaystyle t_A = \frac{L}{V_A} + \frac{1}{3} hr$. (Note I changed to hours to make the units consistent.)
Assume Boy-B doesn't stop, $\displaystyle t_B = \frac{L}{V_B}$.
"[Boy-A] still completes the 30km walk 2hrs before Boy-B."
$t_A = t_B - 2~hr$


I hope this helps.
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