question archive Without actually solving the? problem, choose the correct solution by deciding which choice satisfies the given conditions
Without actually solving the? problem, choose the correct solution by deciding which choice satisfies the given conditions
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Without actually solving the? problem, choose the correct solution by deciding which choice satisfies the given conditions.
The length of a rectangle is 2 feet longer than the width. The perimeter is 20 feet. Find the dimensions of the rectangle. Length= ?; width=?
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of? $9.50 for each? piece, but later decreased the price of each piece by? $2. If they sold all 90 pieces and took in ?$703?, find how many pieces they sold at the original price and how many pieces they sold at the reduced price.
Use a system of equations describing the situation. Do not solve the system.
Two numbers add up to 14 and have a difference of 4.
Gabe? Amodeo, a nuclear? physicist, needs 60 liters of a 60?% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60?% acid? solution?
Gabe needs ? liters of the 40?% solution.
He also needs ? liters of the 70?% solution.
Two high speed trains are 360 miles apart and traveling toward each other. They meet in 5 hours. If one? train's speed is 10 miles per hour faster than the? other, find the speed of each train.
The speed of the slower train is ? mph. ?(Round to two decimal places as? needed.)
The speed of the faster train is ? mph. ?(Round to two decimal places as? needed.)
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Formulate the equations on the basis of question given and solve accordingly.
Step-by-step explanation
1) ?l=w+2?
Perimeter = 20
?2(l+w)=20?
?l+w=10?
?w+2+w=10?
?2w+2=10?
?2w=10−2?
?2w=8?
?w=4?
?l=4+2=6?
The length of rectangle is 6 and width is 4
2) Let the pottery sold at original price be 'x' and at reduced price be 'y'
?x+y=90? ..................(i)
?9.50x+(9.50−2)y=703?
?9.50x+7.50y=703?
?9.50(90−y)+7.50y=703? [ from (i)]
?855−9.50y+7.50y=703?
?−2y=703−855?
?−2y=−152?
?y=76?
?x=90−76=14?
The pottery sold at original price are 14 and at reduced price are 76
3) Let the number be 'x' and 'y'
?x+y=14? .........(i)
?x−y=4?
?x=4+y? .............(ii)
put it in (i)
?4+y+y=14?
?4+2y=14?
?2y=14−4?
?2y=10?
?y=5?
?x=4+5=9?
4) 40% of x + 70% of (60-x) = 60% of 60
?0.4x+0.7(60−x)=0.6∗60?
?0.4x+42−0.7x=36?
?−0.3x=36−42?
?−0.3x=−6?
?x=20?
20 litres of 40%
and (60-20)=40 litres of 70%
5) speed of first train be x
speed of other train = ?x−10?
??speed=timedistance????
?x+x−10=5360??
?2x−10=72?
?2x=72+10?
?2x=82?
?x=41?
speed of first train is 41 miles per hour
and speed of other train is (41-10)=31 miles per hour
