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HELP ME OUT PLEASE SOLVE IT ......................................................application of system equation

(1)An oil painting is in the shape of a rectangle.The perimeter of the painting is 127.4 inches, and the lenght of the painting is 1.6 times the width of the painting.Find the dimensions of the painting.

(2)Maria invested $5500 in two mutual funds.One fund earned an 8% profit,while the other earned a 1.5% profit.Between the two accounts,Maria made a profit of $180. How much was invested in each account?

(3) Raheem can buy peanuts for $0.40 per pound and cashews for $1.05 per pound.How many pounds of each type should he buy to produce 120 pounds of a mixture that costs him $0.66 per pound?

(4) Tina needs 302 inches of fabric to use as binding around a rectagular quilt she is making .The Width of the quilt is 10 inches less than the length of the quilt. Find the dimensions of the quilt
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3 Answers

1) w=width, 1.6w=length
  perimeter=2w+2(1.6w)
                 =2w+3.2w
                 =5.2w
127.4=5.2w
w=127.4/5.2
w=24.5 in
length=1.6*24.5
          =39.2 in
answer: 24.5in by 39.2 in
check:127.4=2(24.5)+2(39.2)
                   =49+78.4
                   =127.4
 
2) let x=amount invested at 8% and (5500-x) amount invested at 1.5%
    180=8%x+1.5%(5500-x)
    180=0.08x+0.015(5500-x)
    180=0.08x+82.5-0.015x
    180=0.065x+82.5
    97.5=0.065x
    x=97.5/0.065
    x=$1500 invested at 8%
    $5500-$1500=$4000 invested at 1.5%
 
 
3) x= # of pounds at $0.40 per pound and y=# 0f pounds at $1.05 per pound
    x+y=120 and y=120-x
    .4x+1.05(120-x)=120(.66)
    .4x+126-1.05x=79.2
    -.65x+126=79.2
    -.65x=-46.8
     0.65x=46.8
        65x=4680
            x=4680/65
            x=72
            y=120-72
            y=48
check: $0.40*72+$1.05*48=120*$0.66
               $28.80+$50.40=$79.20
              $79.20=$79.20
 
 
4)  let L=length
          L-10=width
        2L+2(L-10)=302
        2L+2L-20=302
        4L=322
          L=80.5 in
         W=70.5 in
            
 
   
 
Ibadan,
 
I already answered questions 2 or 3 on previous post
 
I will help set up the problems by helping you get the eqns but I will leave the solving to you
 
In all word problems you need to list the information you have and assign variables to those that you need to solve for
 
(1) P = perimeter of painting = 2L + 2W = 127.4 inches
L = Length of painting = 1.6 W
W = Width of painting
 
substitute
P = 2L + 2W
127.4 = 2(1.6W) + 2W
127.4 = 3.2W + 2W
127.4 = 5.2 W
W = 24.5
L = 1.6 W = 1.6 * 24.5 = 39.2
 
Verify
 
2L + 2 W = 2(24.5) + 2 (39.2) = 49 + 78.2 = 127.4
 
So your answer would be width = 24.5 inches length = 39.2 inches
 
(2) & (3) prev post
 
(4) I'll set this one up you will need to solve, remember units are part of your answer
 
B = binding = 302 inches  
W = width of quilt  = (L-10)
L = length of quilt
 
In case you don't know what the binding is, it is the piece of fabric that goes along the edges of the quilt. hmmm sounds like the perimeter. Yep, you are right
 
B = 2L + 2W = 2L + 2(L-10)
 
 
Now solve for L, than for W and verify that 2L + 2W = 302 inches
 
Good luck
(P = perimeter, w = width, L = length, * is multiply)
 
given:
P = 127.4           (total perimeter) 
P = 2*w + 2*L    (rectangle 4 sides, 2 * width + 2 * Length)
L = 1.6*w           (length is 1.6 * w)
==================================================
solve:
 
(set the two P equations above equal to each other)
P = 127.4 = 2*w + 2*L
 
substitute for L with 1.6*w
 
P = 127.4 = 2*w + 2*(1.6*w) 
 
combine the w terms
P = 127.4 = 5.2*w 
 
solve for w
w = 127.4/5.2 = 24.5  <==
 
solve for L
L = 1.6*24.5   = 39.2  <==
 
check:
P = 2*w + 2*L
P = 2*24.5 + 2*39.2  = 127.4  !!    it checks