Math

QuestionFind the cost of a car wash when 1.4(s+8)=4.2s+61.4(s+8) = 4.2s + 6. Round to the nearest dollar. Options: \$2, \$10, \$14, \$19.

Studdy Solution

STEP 1

Assumptions1. The cost of a car wash at Speedy Wash is represented by the expression 1.4(s+8)1.4(s+8). The cost of a car wash at Soapy Suds is represented by the expression 4.s+64.s+6
3. The cost of a car wash is the same at both locations4. The variable ss represents the cost of supplies

STEP 2

Since the cost of a car wash is the same at both locations, we can set the two expressions equal to each other and solve for ss.
1.4(s+8)=4.2s+61.4(s+8) =4.2s +6

STEP 3

istribute the 1.1. on the left side of the equation.
1.s+11.2=.2s+61.s +11.2 =.2s +6

STEP 4

Subtract 1.4s1.4s from both sides of the equation to isolate ss on one side.
11.2=2.8s+611.2 =2.8s +6

STEP 5

Subtract $$ from both sides of the equation.
5.2=2.8s5.2 =2.8s

STEP 6

Divide both sides of the equation by 2.82.8 to solve for ss.
s=5.22.8s = \frac{5.2}{2.8}

STEP 7

Calculate the value of ss.
s1.857s \approx1.857

STEP 8

Now that we have the cost of supplies, we can substitute this value back into either of the original expressions to find the cost of each wash. Let's use the expression for Speedy Wash.
Cost=1.4(s+8)Cost =1.4(s+8)

STEP 9

Substitute the value of ss into the expression.
Cost=.4(.857+8)Cost =.4(.857+8)

STEP 10

Calculate the value inside the parentheses.
Cost=.4×9.857Cost =.4 \times9.857

STEP 11

Calculate the cost of each wash.
Cost.4×9.857=13.8Cost \approx.4 \times9.857 =13.8Rounding to the nearest dollar, each wash costs $14\$14.

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